xref: /libCEED/interface/ceed-preconditioning.c (revision 1203703b5dc87b4acbe66c9a27384ca8ad07798d)
1 // Copyright (c) 2017-2022, Lawrence Livermore National Security, LLC and other CEED contributors.
2 // All Rights Reserved. See the top-level LICENSE and NOTICE files for details.
3 //
4 // SPDX-License-Identifier: BSD-2-Clause
5 //
6 // This file is part of CEED:  http://github.com/ceed
7 
8 #include <ceed-impl.h>
9 #include <ceed.h>
10 #include <ceed/backend.h>
11 #include <assert.h>
12 #include <math.h>
13 #include <stdbool.h>
14 #include <stdio.h>
15 #include <string.h>
16 
17 /// @file
18 /// Implementation of CeedOperator preconditioning interfaces
19 
20 /// ----------------------------------------------------------------------------
21 /// CeedOperator Library Internal Preconditioning Functions
22 /// ----------------------------------------------------------------------------
23 /// @addtogroup CeedOperatorDeveloper
24 /// @{
25 
26 /**
27   @brief Duplicate a `CeedQFunction` with a reference `Ceed` to fallback for advanced `CeedOperator` functionality
28 
29   @param[in]  fallback_ceed `Ceed` on which to create fallback `CeedQFunction`
30   @param[in]  qf            `CeedQFunction` to create fallback for
31   @param[out] qf_fallback   Fallback `CeedQFunction`
32 
33   @return An error code: 0 - success, otherwise - failure
34 
35   @ref Developer
36 **/
37 static int CeedQFunctionCreateFallback(Ceed fallback_ceed, CeedQFunction qf, CeedQFunction *qf_fallback) {
38   char               *source_path_with_name = NULL;
39   CeedInt             num_input_fields, num_output_fields;
40   Ceed                ceed;
41   CeedQFunctionField *input_fields, *output_fields;
42 
43   // Check if NULL qf passed in
44   if (!qf) return CEED_ERROR_SUCCESS;
45 
46   CeedCall(CeedQFunctionGetCeed(qf, &ceed));
47   CeedDebug256(ceed, 1, "---------- CeedOperator Fallback ----------\n");
48   CeedDebug(ceed, "Creating fallback CeedQFunction\n");
49 
50   if (qf->source_path) {
51     size_t path_len = strlen(qf->source_path), name_len = strlen(qf->kernel_name);
52     CeedCall(CeedCalloc(path_len + name_len + 2, &source_path_with_name));
53     memcpy(source_path_with_name, qf->source_path, path_len);
54     memcpy(&source_path_with_name[path_len], ":", 1);
55     memcpy(&source_path_with_name[path_len + 1], qf->kernel_name, name_len);
56   } else {
57     CeedCall(CeedCalloc(1, &source_path_with_name));
58   }
59 
60   {
61     CeedInt           vec_length;
62     CeedQFunctionUser f;
63 
64     CeedCall(CeedQFunctionGetVectorLength(qf, &vec_length));
65     CeedCall(CeedQFunctionGetUserFunction(qf, &f));
66     CeedCall(CeedQFunctionCreateInterior(fallback_ceed, vec_length, f, source_path_with_name, qf_fallback));
67   }
68   {
69     CeedQFunctionContext ctx;
70 
71     CeedCall(CeedQFunctionGetContext(qf, &ctx));
72     CeedCall(CeedQFunctionSetContext(*qf_fallback, ctx));
73   }
74   CeedCall(CeedQFunctionGetFields(qf, &num_input_fields, &input_fields, &num_output_fields, &output_fields));
75   for (CeedInt i = 0; i < num_input_fields; i++) {
76     char        *field_name;
77     CeedInt      size;
78     CeedEvalMode eval_mode;
79 
80     CeedCall(CeedQFunctionFieldGetName(input_fields[i], &field_name));
81     CeedCall(CeedQFunctionFieldGetSize(input_fields[i], &size));
82     CeedCall(CeedQFunctionFieldGetEvalMode(input_fields[i], &eval_mode));
83     CeedCall(CeedQFunctionAddInput(*qf_fallback, field_name, size, eval_mode));
84   }
85   for (CeedInt i = 0; i < num_output_fields; i++) {
86     char        *field_name;
87     CeedInt      size;
88     CeedEvalMode eval_mode;
89 
90     CeedCall(CeedQFunctionFieldGetName(output_fields[i], &field_name));
91     CeedCall(CeedQFunctionFieldGetSize(output_fields[i], &size));
92     CeedCall(CeedQFunctionFieldGetEvalMode(output_fields[i], &eval_mode));
93     CeedCall(CeedQFunctionAddOutput(*qf_fallback, field_name, size, eval_mode));
94   }
95   CeedCall(CeedFree(&source_path_with_name));
96   return CEED_ERROR_SUCCESS;
97 }
98 
99 /**
100   @brief Duplicate a `CeedOperator` with a reference `Ceed` to fallback for advanced `CeedOperator` functionality
101 
102   @param[in,out] op `CeedOperator` to create fallback for
103 
104   @return An error code: 0 - success, otherwise - failure
105 
106   @ref Developer
107 **/
108 static int CeedOperatorCreateFallback(CeedOperator op) {
109   bool         is_composite;
110   Ceed         ceed, ceed_fallback;
111   CeedOperator op_fallback;
112 
113   // Check not already created
114   if (op->op_fallback) return CEED_ERROR_SUCCESS;
115 
116   // Fallback Ceed
117   CeedCall(CeedOperatorGetCeed(op, &ceed));
118   CeedCall(CeedGetOperatorFallbackCeed(ceed, &ceed_fallback));
119   if (!ceed_fallback) return CEED_ERROR_SUCCESS;
120 
121   CeedDebug256(ceed, 1, "---------- CeedOperator Fallback ----------\n");
122   CeedDebug(ceed, "Creating fallback CeedOperator\n");
123 
124   // Clone Op
125   CeedCall(CeedOperatorIsComposite(op, &is_composite));
126   if (is_composite) {
127     CeedInt       num_suboperators;
128     CeedOperator *sub_operators;
129 
130     CeedCall(CeedCompositeOperatorCreate(ceed_fallback, &op_fallback));
131     CeedCall(CeedCompositeOperatorGetNumSub(op, &num_suboperators));
132     CeedCall(CeedCompositeOperatorGetSubList(op, &sub_operators));
133     for (CeedInt i = 0; i < num_suboperators; i++) {
134       CeedOperator op_sub_fallback;
135 
136       CeedCall(CeedOperatorGetFallback(sub_operators[i], &op_sub_fallback));
137       CeedCall(CeedCompositeOperatorAddSub(op_fallback, op_sub_fallback));
138     }
139   } else {
140     CeedInt            num_input_fields, num_output_fields;
141     CeedQFunction      qf_fallback = NULL, dqf_fallback = NULL, dqfT_fallback = NULL;
142     CeedOperatorField *input_fields, *output_fields;
143 
144     CeedCall(CeedQFunctionCreateFallback(ceed_fallback, op->qf, &qf_fallback));
145     CeedCall(CeedQFunctionCreateFallback(ceed_fallback, op->dqf, &dqf_fallback));
146     CeedCall(CeedQFunctionCreateFallback(ceed_fallback, op->dqfT, &dqfT_fallback));
147     CeedCall(CeedOperatorCreate(ceed_fallback, qf_fallback, dqf_fallback, dqfT_fallback, &op_fallback));
148     CeedCall(CeedOperatorGetFields(op, &num_input_fields, &input_fields, &num_output_fields, &output_fields));
149     for (CeedInt i = 0; i < num_input_fields; i++) {
150       char               *field_name;
151       CeedVector          vec;
152       CeedElemRestriction rstr;
153       CeedBasis           basis;
154 
155       CeedCall(CeedOperatorFieldGetName(input_fields[i], &field_name));
156       CeedCall(CeedOperatorFieldGetVector(input_fields[i], &vec));
157       CeedCall(CeedOperatorFieldGetElemRestriction(input_fields[i], &rstr));
158       CeedCall(CeedOperatorFieldGetBasis(input_fields[i], &basis));
159       CeedCall(CeedOperatorSetField(op_fallback, field_name, rstr, basis, vec));
160     }
161     for (CeedInt i = 0; i < num_output_fields; i++) {
162       char               *field_name;
163       CeedVector          vec;
164       CeedElemRestriction rstr;
165       CeedBasis           basis;
166 
167       CeedCall(CeedOperatorFieldGetName(output_fields[i], &field_name));
168       CeedCall(CeedOperatorFieldGetVector(output_fields[i], &vec));
169       CeedCall(CeedOperatorFieldGetElemRestriction(output_fields[i], &rstr));
170       CeedCall(CeedOperatorFieldGetBasis(output_fields[i], &basis));
171       CeedCall(CeedOperatorSetField(op_fallback, field_name, rstr, basis, vec));
172     }
173     CeedCall(CeedQFunctionAssemblyDataReferenceCopy(op->qf_assembled, &op_fallback->qf_assembled));
174     // Cleanup
175     CeedCall(CeedQFunctionDestroy(&qf_fallback));
176     CeedCall(CeedQFunctionDestroy(&dqf_fallback));
177     CeedCall(CeedQFunctionDestroy(&dqfT_fallback));
178   }
179   CeedCall(CeedOperatorSetName(op_fallback, op->name));
180   CeedCall(CeedOperatorCheckReady(op_fallback));
181   // Note: No ref-counting here so we don't get caught in a reference loop.
182   //       The op holds the only reference to op_fallback and is responsible for deleting itself and op_fallback.
183   op->op_fallback                 = op_fallback;
184   op_fallback->op_fallback_parent = op;
185   return CEED_ERROR_SUCCESS;
186 }
187 
188 /**
189   @brief Core logic for assembling operator diagonal or point block diagonal
190 
191   @param[in]  op             `CeedOperator` to assemble point block diagonal
192   @param[in]  request        Address of @ref CeedRequest for non-blocking completion, else @ref CEED_REQUEST_IMMEDIATE
193   @param[in]  is_point_block Boolean flag to assemble diagonal or point block diagonal
194   @param[out] assembled      `CeedVector` to store assembled diagonal
195 
196   @return An error code: 0 - success, otherwise - failure
197 
198   @ref Developer
199 **/
200 static inline int CeedSingleOperatorAssembleAddDiagonal_Core(CeedOperator op, CeedRequest *request, const bool is_point_block, CeedVector assembled) {
201   Ceed ceed;
202   bool is_composite;
203 
204   CeedCall(CeedOperatorGetCeed(op, &ceed));
205   CeedCall(CeedOperatorIsComposite(op, &is_composite));
206   CeedCheck(!is_composite, ceed, CEED_ERROR_UNSUPPORTED, "Composite operator not supported");
207 
208   // Assemble QFunction
209   CeedInt             layout_qf[3];
210   const CeedScalar   *assembled_qf_array;
211   CeedVector          assembled_qf        = NULL;
212   CeedElemRestriction assembled_elem_rstr = NULL;
213 
214   CeedCall(CeedOperatorLinearAssembleQFunctionBuildOrUpdate(op, &assembled_qf, &assembled_elem_rstr, request));
215   CeedCall(CeedElemRestrictionGetELayout(assembled_elem_rstr, layout_qf));
216   CeedCall(CeedElemRestrictionDestroy(&assembled_elem_rstr));
217   CeedCall(CeedVectorGetArrayRead(assembled_qf, CEED_MEM_HOST, &assembled_qf_array));
218 
219   // Get assembly data
220   const CeedEvalMode     **eval_modes_in, **eval_modes_out;
221   CeedInt                  num_active_bases_in, *num_eval_modes_in, num_active_bases_out, *num_eval_modes_out;
222   CeedSize               **eval_mode_offsets_in, **eval_mode_offsets_out, num_output_components;
223   CeedBasis               *active_bases_in, *active_bases_out;
224   CeedElemRestriction     *active_elem_rstrs_in, *active_elem_rstrs_out;
225   CeedOperatorAssemblyData data;
226 
227   CeedCall(CeedOperatorGetOperatorAssemblyData(op, &data));
228   CeedCall(CeedOperatorAssemblyDataGetEvalModes(data, &num_active_bases_in, &num_eval_modes_in, &eval_modes_in, &eval_mode_offsets_in,
229                                                 &num_active_bases_out, &num_eval_modes_out, &eval_modes_out, &eval_mode_offsets_out,
230                                                 &num_output_components));
231   CeedCall(CeedOperatorAssemblyDataGetBases(data, NULL, &active_bases_in, NULL, NULL, &active_bases_out, NULL));
232   CeedCall(CeedOperatorAssemblyDataGetElemRestrictions(data, NULL, &active_elem_rstrs_in, NULL, &active_elem_rstrs_out));
233 
234   // Loop over all active bases (find matching input/output pairs)
235   for (CeedInt b = 0; b < CeedIntMin(num_active_bases_in, num_active_bases_out); b++) {
236     CeedInt             b_in, b_out, num_elem, num_nodes, num_qpts, num_comp;
237     bool                has_eval_none = false;
238     CeedScalar         *elem_diag_array, *identity = NULL;
239     CeedVector          elem_diag;
240     CeedElemRestriction diag_elem_rstr;
241 
242     if (num_active_bases_in <= num_active_bases_out) {
243       b_in = b;
244       for (b_out = 0; b_out < num_active_bases_out; b_out++) {
245         if (active_bases_in[b_in] == active_bases_out[b_out]) {
246           break;
247         }
248       }
249       if (b_out == num_active_bases_out) {
250         continue;
251       }  // No matching output basis found
252     } else {
253       b_out = b;
254       for (b_in = 0; b_in < num_active_bases_in; b_in++) {
255         if (active_bases_in[b_in] == active_bases_out[b_out]) {
256           break;
257         }
258       }
259       if (b_in == num_active_bases_in) {
260         continue;
261       }  // No matching output basis found
262     }
263     CeedCheck(active_elem_rstrs_in[b_in] == active_elem_rstrs_out[b_out], ceed, CEED_ERROR_UNSUPPORTED,
264               "Cannot assemble operator diagonal with different input and output active element restrictions");
265 
266     // Assemble point block diagonal restriction, if needed
267     if (is_point_block) {
268       CeedCall(CeedOperatorCreateActivePointBlockRestriction(active_elem_rstrs_in[b_in], &diag_elem_rstr));
269     } else {
270       CeedCall(CeedElemRestrictionCreateUnsignedCopy(active_elem_rstrs_in[b_in], &diag_elem_rstr));
271     }
272 
273     // Create diagonal vector
274     CeedCall(CeedElemRestrictionCreateVector(diag_elem_rstr, NULL, &elem_diag));
275 
276     // Assemble element operator diagonals
277     CeedCall(CeedVectorSetValue(elem_diag, 0.0));
278     CeedCall(CeedVectorGetArray(elem_diag, CEED_MEM_HOST, &elem_diag_array));
279     CeedCall(CeedElemRestrictionGetNumElements(diag_elem_rstr, &num_elem));
280     CeedCall(CeedBasisGetNumNodes(active_bases_in[b_in], &num_nodes));
281     CeedCall(CeedBasisGetNumComponents(active_bases_in[b_in], &num_comp));
282     if (active_bases_in[b_in] == CEED_BASIS_NONE) num_qpts = num_nodes;
283     else CeedCall(CeedBasisGetNumQuadraturePoints(active_bases_in[b_in], &num_qpts));
284 
285     // Construct identity matrix for basis if required
286     for (CeedInt i = 0; i < num_eval_modes_in[b_in]; i++) {
287       has_eval_none = has_eval_none || (eval_modes_in[b_in][i] == CEED_EVAL_NONE);
288     }
289     for (CeedInt i = 0; i < num_eval_modes_out[b_out]; i++) {
290       has_eval_none = has_eval_none || (eval_modes_out[b_out][i] == CEED_EVAL_NONE);
291     }
292     if (has_eval_none) {
293       CeedCall(CeedCalloc(num_qpts * num_nodes, &identity));
294       for (CeedInt i = 0; i < (num_nodes < num_qpts ? num_nodes : num_qpts); i++) identity[i * num_nodes + i] = 1.0;
295     }
296 
297     // Compute the diagonal of B^T D B
298     // Each element
299     for (CeedSize e = 0; e < num_elem; e++) {
300       // Each basis eval mode pair
301       CeedInt      d_out              = 0, q_comp_out;
302       CeedEvalMode eval_mode_out_prev = CEED_EVAL_NONE;
303 
304       for (CeedInt e_out = 0; e_out < num_eval_modes_out[b_out]; e_out++) {
305         CeedInt           d_in              = 0, q_comp_in;
306         const CeedScalar *B_t               = NULL;
307         CeedEvalMode      eval_mode_in_prev = CEED_EVAL_NONE;
308 
309         CeedCall(CeedOperatorGetBasisPointer(active_bases_out[b_out], eval_modes_out[b_out][e_out], identity, &B_t));
310         CeedCall(CeedBasisGetNumQuadratureComponents(active_bases_out[b_out], eval_modes_out[b_out][e_out], &q_comp_out));
311         if (q_comp_out > 1) {
312           if (e_out == 0 || eval_modes_out[b_out][e_out] != eval_mode_out_prev) d_out = 0;
313           else B_t = &B_t[(++d_out) * num_qpts * num_nodes];
314         }
315         eval_mode_out_prev = eval_modes_out[b_out][e_out];
316 
317         for (CeedInt e_in = 0; e_in < num_eval_modes_in[b_in]; e_in++) {
318           const CeedScalar *B = NULL;
319 
320           CeedCall(CeedOperatorGetBasisPointer(active_bases_in[b_in], eval_modes_in[b_in][e_in], identity, &B));
321           CeedCall(CeedBasisGetNumQuadratureComponents(active_bases_in[b_in], eval_modes_in[b_in][e_in], &q_comp_in));
322           if (q_comp_in > 1) {
323             if (e_in == 0 || eval_modes_in[b_in][e_in] != eval_mode_in_prev) d_in = 0;
324             else B = &B[(++d_in) * num_qpts * num_nodes];
325           }
326           eval_mode_in_prev = eval_modes_in[b_in][e_in];
327 
328           // Each component
329           for (CeedInt c_out = 0; c_out < num_comp; c_out++) {
330             // Each qpt/node pair
331             for (CeedInt q = 0; q < num_qpts; q++) {
332               if (is_point_block) {
333                 // Point Block Diagonal
334                 for (CeedInt c_in = 0; c_in < num_comp; c_in++) {
335                   const CeedSize c_offset =
336                       (eval_mode_offsets_in[b_in][e_in] + c_in) * num_output_components + eval_mode_offsets_out[b_out][e_out] + c_out;
337                   const CeedScalar qf_value = assembled_qf_array[q * layout_qf[0] + c_offset * layout_qf[1] + e * layout_qf[2]];
338 
339                   for (CeedInt n = 0; n < num_nodes; n++) {
340                     elem_diag_array[((e * num_comp + c_out) * num_comp + c_in) * num_nodes + n] +=
341                         B_t[q * num_nodes + n] * qf_value * B[q * num_nodes + n];
342                   }
343                 }
344               } else {
345                 // Diagonal Only
346                 const CeedInt c_offset =
347                     (eval_mode_offsets_in[b_in][e_in] + c_out) * num_output_components + eval_mode_offsets_out[b_out][e_out] + c_out;
348                 const CeedScalar qf_value = assembled_qf_array[q * layout_qf[0] + c_offset * layout_qf[1] + e * layout_qf[2]];
349 
350                 for (CeedInt n = 0; n < num_nodes; n++) {
351                   elem_diag_array[(e * num_comp + c_out) * num_nodes + n] += B_t[q * num_nodes + n] * qf_value * B[q * num_nodes + n];
352                 }
353               }
354             }
355           }
356         }
357       }
358     }
359     CeedCall(CeedVectorRestoreArray(elem_diag, &elem_diag_array));
360 
361     // Assemble local operator diagonal
362     CeedCall(CeedElemRestrictionApply(diag_elem_rstr, CEED_TRANSPOSE, elem_diag, assembled, request));
363 
364     // Cleanup
365     CeedCall(CeedElemRestrictionDestroy(&diag_elem_rstr));
366     CeedCall(CeedVectorDestroy(&elem_diag));
367     CeedCall(CeedFree(&identity));
368   }
369   CeedCall(CeedVectorRestoreArrayRead(assembled_qf, &assembled_qf_array));
370   CeedCall(CeedVectorDestroy(&assembled_qf));
371   return CEED_ERROR_SUCCESS;
372 }
373 
374 /**
375   @brief Core logic for assembling composite operator diagonal
376 
377   @param[in]  op             `CeedOperator` to assemble point block diagonal
378   @param[in]  request        Address of @ref CeedRequest for non-blocking completion, else @ref CEED_REQUEST_IMMEDIATE
379   @param[in]  is_point_block Boolean flag to assemble diagonal or point block diagonal
380   @param[out] assembled      `CeedVector` to store assembled diagonal
381 
382   @return An error code: 0 - success, otherwise - failure
383 
384   @ref Developer
385 **/
386 static inline int CeedCompositeOperatorLinearAssembleAddDiagonal(CeedOperator op, CeedRequest *request, const bool is_point_block,
387                                                                  CeedVector assembled) {
388   CeedInt       num_sub;
389   CeedOperator *suboperators;
390 
391   CeedCall(CeedCompositeOperatorGetNumSub(op, &num_sub));
392   CeedCall(CeedCompositeOperatorGetSubList(op, &suboperators));
393   for (CeedInt i = 0; i < num_sub; i++) {
394     if (is_point_block) {
395       CeedCall(CeedOperatorLinearAssembleAddPointBlockDiagonal(suboperators[i], assembled, request));
396     } else {
397       CeedCall(CeedOperatorLinearAssembleAddDiagonal(suboperators[i], assembled, request));
398     }
399   }
400   return CEED_ERROR_SUCCESS;
401 }
402 
403 /**
404   @brief Build nonzero pattern for non-composite CeedOperator`.
405 
406   Users should generally use @ref CeedOperatorLinearAssembleSymbolic().
407 
408   @param[in]  op     `CeedOperator` to assemble nonzero pattern
409   @param[in]  offset Offset for number of entries
410   @param[out] rows   Row number for each entry
411   @param[out] cols   Column number for each entry
412 
413   @return An error code: 0 - success, otherwise - failure
414 
415   @ref Developer
416 **/
417 static int CeedSingleOperatorAssembleSymbolic(CeedOperator op, CeedInt offset, CeedInt *rows, CeedInt *cols) {
418   Ceed                ceed;
419   bool                is_composite;
420   CeedSize            num_nodes_in, num_nodes_out, count = 0;
421   CeedInt             num_elem_in, elem_size_in, num_comp_in, layout_er_in[3];
422   CeedInt             num_elem_out, elem_size_out, num_comp_out, layout_er_out[3], local_num_entries;
423   CeedScalar         *array;
424   const CeedScalar   *elem_dof_a_in, *elem_dof_a_out;
425   CeedVector          index_vec_in, index_vec_out, elem_dof_in, elem_dof_out;
426   CeedElemRestriction elem_rstr_in, elem_rstr_out, index_elem_rstr_in, index_elem_rstr_out;
427 
428   CeedCall(CeedOperatorGetCeed(op, &ceed));
429   CeedCall(CeedOperatorIsComposite(op, &is_composite));
430   CeedCheck(!is_composite, ceed, CEED_ERROR_UNSUPPORTED, "Composite operator not supported");
431 
432   CeedCall(CeedOperatorGetActiveVectorLengths(op, &num_nodes_in, &num_nodes_out));
433   CeedCall(CeedOperatorGetActiveElemRestrictions(op, &elem_rstr_in, &elem_rstr_out));
434   CeedCall(CeedElemRestrictionGetNumElements(elem_rstr_in, &num_elem_in));
435   CeedCall(CeedElemRestrictionGetElementSize(elem_rstr_in, &elem_size_in));
436   CeedCall(CeedElemRestrictionGetNumComponents(elem_rstr_in, &num_comp_in));
437   CeedCall(CeedElemRestrictionGetELayout(elem_rstr_in, layout_er_in));
438 
439   // Determine elem_dof relation for input
440   CeedCall(CeedVectorCreate(ceed, num_nodes_in, &index_vec_in));
441   CeedCall(CeedVectorGetArrayWrite(index_vec_in, CEED_MEM_HOST, &array));
442   for (CeedInt i = 0; i < num_nodes_in; i++) array[i] = i;
443   CeedCall(CeedVectorRestoreArray(index_vec_in, &array));
444   CeedCall(CeedVectorCreate(ceed, num_elem_in * elem_size_in * num_comp_in, &elem_dof_in));
445   CeedCall(CeedVectorSetValue(elem_dof_in, 0.0));
446   CeedCall(CeedElemRestrictionCreateUnorientedCopy(elem_rstr_in, &index_elem_rstr_in));
447   CeedCall(CeedElemRestrictionApply(index_elem_rstr_in, CEED_NOTRANSPOSE, index_vec_in, elem_dof_in, CEED_REQUEST_IMMEDIATE));
448   CeedCall(CeedVectorGetArrayRead(elem_dof_in, CEED_MEM_HOST, &elem_dof_a_in));
449   CeedCall(CeedVectorDestroy(&index_vec_in));
450   CeedCall(CeedElemRestrictionDestroy(&index_elem_rstr_in));
451 
452   if (elem_rstr_in != elem_rstr_out) {
453     CeedCall(CeedElemRestrictionGetNumElements(elem_rstr_out, &num_elem_out));
454     CeedCheck(num_elem_in == num_elem_out, ceed, CEED_ERROR_UNSUPPORTED,
455               "Active input and output operator restrictions must have the same number of elements");
456     CeedCall(CeedElemRestrictionGetElementSize(elem_rstr_out, &elem_size_out));
457     CeedCall(CeedElemRestrictionGetNumComponents(elem_rstr_out, &num_comp_out));
458     CeedCall(CeedElemRestrictionGetELayout(elem_rstr_out, layout_er_out));
459 
460     // Determine elem_dof relation for output
461     CeedCall(CeedVectorCreate(ceed, num_nodes_out, &index_vec_out));
462     CeedCall(CeedVectorGetArrayWrite(index_vec_out, CEED_MEM_HOST, &array));
463     for (CeedInt i = 0; i < num_nodes_out; i++) array[i] = i;
464     CeedCall(CeedVectorRestoreArray(index_vec_out, &array));
465     CeedCall(CeedVectorCreate(ceed, num_elem_out * elem_size_out * num_comp_out, &elem_dof_out));
466     CeedCall(CeedVectorSetValue(elem_dof_out, 0.0));
467     CeedCall(CeedElemRestrictionCreateUnorientedCopy(elem_rstr_out, &index_elem_rstr_out));
468     CeedCall(CeedElemRestrictionApply(index_elem_rstr_out, CEED_NOTRANSPOSE, index_vec_out, elem_dof_out, CEED_REQUEST_IMMEDIATE));
469     CeedCall(CeedVectorGetArrayRead(elem_dof_out, CEED_MEM_HOST, &elem_dof_a_out));
470     CeedCall(CeedVectorDestroy(&index_vec_out));
471     CeedCall(CeedElemRestrictionDestroy(&index_elem_rstr_out));
472   } else {
473     num_elem_out     = num_elem_in;
474     elem_size_out    = elem_size_in;
475     num_comp_out     = num_comp_in;
476     layout_er_out[0] = layout_er_in[0];
477     layout_er_out[1] = layout_er_in[1];
478     layout_er_out[2] = layout_er_in[2];
479     elem_dof_a_out   = elem_dof_a_in;
480   }
481   local_num_entries = elem_size_out * num_comp_out * elem_size_in * num_comp_in * num_elem_in;
482 
483   // Determine i, j locations for element matrices
484   for (CeedInt e = 0; e < num_elem_in; e++) {
485     for (CeedInt comp_in = 0; comp_in < num_comp_in; comp_in++) {
486       for (CeedInt comp_out = 0; comp_out < num_comp_out; comp_out++) {
487         for (CeedInt i = 0; i < elem_size_out; i++) {
488           for (CeedInt j = 0; j < elem_size_in; j++) {
489             const CeedInt elem_dof_index_row = i * layout_er_out[0] + comp_out * layout_er_out[1] + e * layout_er_out[2];
490             const CeedInt elem_dof_index_col = j * layout_er_in[0] + comp_in * layout_er_in[1] + e * layout_er_in[2];
491             const CeedInt row                = elem_dof_a_out[elem_dof_index_row];
492             const CeedInt col                = elem_dof_a_in[elem_dof_index_col];
493 
494             rows[offset + count] = row;
495             cols[offset + count] = col;
496             count++;
497           }
498         }
499       }
500     }
501   }
502   CeedCheck(count == local_num_entries, ceed, CEED_ERROR_MAJOR, "Error computing assembled entries");
503   CeedCall(CeedVectorRestoreArrayRead(elem_dof_in, &elem_dof_a_in));
504   CeedCall(CeedVectorDestroy(&elem_dof_in));
505   if (elem_rstr_in != elem_rstr_out) {
506     CeedCall(CeedVectorRestoreArrayRead(elem_dof_out, &elem_dof_a_out));
507     CeedCall(CeedVectorDestroy(&elem_dof_out));
508   }
509   return CEED_ERROR_SUCCESS;
510 }
511 
512 /**
513   @brief Assemble nonzero entries for non-composite `CeedOperator`.
514 
515   Users should generally use @ref CeedOperatorLinearAssemble().
516 
517   @param[in]  op     `CeedOperator` to assemble
518   @param[in]  offset Offset for number of entries
519   @param[out] values Values to assemble into matrix
520 
521   @return An error code: 0 - success, otherwise - failure
522 
523   @ref Developer
524 **/
525 static int CeedSingleOperatorAssemble(CeedOperator op, CeedInt offset, CeedVector values) {
526   Ceed ceed;
527   bool is_composite;
528 
529   CeedCall(CeedOperatorGetCeed(op, &ceed));
530   CeedCall(CeedOperatorIsComposite(op, &is_composite));
531   CeedCheck(!is_composite, ceed, CEED_ERROR_UNSUPPORTED, "Composite operator not supported");
532 
533   // Early exit for empty operator
534   {
535     CeedInt num_elem = 0;
536 
537     CeedCall(CeedOperatorGetNumElements(op, &num_elem));
538     if (num_elem == 0) return CEED_ERROR_SUCCESS;
539   }
540 
541   if (op->LinearAssembleSingle) {
542     // Backend version
543     CeedCall(op->LinearAssembleSingle(op, offset, values));
544     return CEED_ERROR_SUCCESS;
545   } else {
546     // Operator fallback
547     CeedOperator op_fallback;
548 
549     CeedCall(CeedOperatorGetFallback(op, &op_fallback));
550     if (op_fallback) {
551       CeedCall(CeedSingleOperatorAssemble(op_fallback, offset, values));
552       return CEED_ERROR_SUCCESS;
553     }
554   }
555 
556   // Assemble QFunction
557   CeedInt             layout_qf[3];
558   const CeedScalar   *assembled_qf_array;
559   CeedVector          assembled_qf        = NULL;
560   CeedElemRestriction assembled_elem_rstr = NULL;
561 
562   CeedCall(CeedOperatorLinearAssembleQFunctionBuildOrUpdate(op, &assembled_qf, &assembled_elem_rstr, CEED_REQUEST_IMMEDIATE));
563   CeedCall(CeedElemRestrictionGetELayout(assembled_elem_rstr, layout_qf));
564   CeedCall(CeedElemRestrictionDestroy(&assembled_elem_rstr));
565   CeedCall(CeedVectorGetArrayRead(assembled_qf, CEED_MEM_HOST, &assembled_qf_array));
566 
567   // Get assembly data
568   CeedInt                  num_elem_in, elem_size_in, num_comp_in, num_qpts_in;
569   CeedInt                  num_elem_out, elem_size_out, num_comp_out, num_qpts_out, local_num_entries;
570   const CeedEvalMode     **eval_modes_in, **eval_modes_out;
571   CeedInt                  num_active_bases_in, *num_eval_modes_in, num_active_bases_out, *num_eval_modes_out;
572   CeedBasis               *active_bases_in, *active_bases_out, basis_in, basis_out;
573   const CeedScalar       **B_mats_in, **B_mats_out, *B_mat_in, *B_mat_out;
574   CeedElemRestriction      elem_rstr_in, elem_rstr_out;
575   CeedRestrictionType      elem_rstr_type_in, elem_rstr_type_out;
576   const bool              *elem_rstr_orients_in = NULL, *elem_rstr_orients_out = NULL;
577   const CeedInt8          *elem_rstr_curl_orients_in = NULL, *elem_rstr_curl_orients_out = NULL;
578   CeedOperatorAssemblyData data;
579 
580   CeedCall(CeedOperatorGetOperatorAssemblyData(op, &data));
581   CeedCall(CeedOperatorAssemblyDataGetEvalModes(data, &num_active_bases_in, &num_eval_modes_in, &eval_modes_in, NULL, &num_active_bases_out,
582                                                 &num_eval_modes_out, &eval_modes_out, NULL, NULL));
583 
584   CeedCheck(num_active_bases_in == num_active_bases_out && num_active_bases_in == 1, ceed, CEED_ERROR_UNSUPPORTED,
585             "Cannot assemble operator with multiple active bases");
586   CeedCheck(num_eval_modes_in[0] > 0 && num_eval_modes_out[0] > 0, ceed, CEED_ERROR_UNSUPPORTED, "Cannot assemble operator without inputs/outputs");
587 
588   CeedCall(CeedOperatorAssemblyDataGetBases(data, NULL, &active_bases_in, &B_mats_in, NULL, &active_bases_out, &B_mats_out));
589   CeedCall(CeedOperatorGetActiveElemRestrictions(op, &elem_rstr_in, &elem_rstr_out));
590   basis_in  = active_bases_in[0];
591   basis_out = active_bases_out[0];
592   B_mat_in  = B_mats_in[0];
593   B_mat_out = B_mats_out[0];
594 
595   CeedCall(CeedElemRestrictionGetNumElements(elem_rstr_in, &num_elem_in));
596   CeedCall(CeedElemRestrictionGetElementSize(elem_rstr_in, &elem_size_in));
597   CeedCall(CeedElemRestrictionGetNumComponents(elem_rstr_in, &num_comp_in));
598   if (basis_in == CEED_BASIS_NONE) num_qpts_in = elem_size_in;
599   else CeedCall(CeedBasisGetNumQuadraturePoints(basis_in, &num_qpts_in));
600 
601   CeedCall(CeedElemRestrictionGetType(elem_rstr_in, &elem_rstr_type_in));
602   if (elem_rstr_type_in == CEED_RESTRICTION_ORIENTED) {
603     CeedCall(CeedElemRestrictionGetOrientations(elem_rstr_in, CEED_MEM_HOST, &elem_rstr_orients_in));
604   } else if (elem_rstr_type_in == CEED_RESTRICTION_CURL_ORIENTED) {
605     CeedCall(CeedElemRestrictionGetCurlOrientations(elem_rstr_in, CEED_MEM_HOST, &elem_rstr_curl_orients_in));
606   }
607 
608   if (elem_rstr_in != elem_rstr_out) {
609     CeedCall(CeedElemRestrictionGetNumElements(elem_rstr_out, &num_elem_out));
610     CeedCheck(num_elem_in == num_elem_out, ceed, CEED_ERROR_UNSUPPORTED,
611               "Active input and output operator restrictions must have the same number of elements");
612     CeedCall(CeedElemRestrictionGetElementSize(elem_rstr_out, &elem_size_out));
613     CeedCall(CeedElemRestrictionGetNumComponents(elem_rstr_out, &num_comp_out));
614     if (basis_out == CEED_BASIS_NONE) num_qpts_out = elem_size_out;
615     else CeedCall(CeedBasisGetNumQuadraturePoints(basis_out, &num_qpts_out));
616     CeedCheck(num_qpts_in == num_qpts_out, ceed, CEED_ERROR_UNSUPPORTED,
617               "Active input and output bases must have the same number of quadrature points");
618 
619     CeedCall(CeedElemRestrictionGetType(elem_rstr_out, &elem_rstr_type_out));
620     if (elem_rstr_type_out == CEED_RESTRICTION_ORIENTED) {
621       CeedCall(CeedElemRestrictionGetOrientations(elem_rstr_out, CEED_MEM_HOST, &elem_rstr_orients_out));
622     } else if (elem_rstr_type_out == CEED_RESTRICTION_CURL_ORIENTED) {
623       CeedCall(CeedElemRestrictionGetCurlOrientations(elem_rstr_out, CEED_MEM_HOST, &elem_rstr_curl_orients_out));
624     }
625   } else {
626     num_elem_out  = num_elem_in;
627     elem_size_out = elem_size_in;
628     num_comp_out  = num_comp_in;
629     num_qpts_out  = num_qpts_in;
630 
631     elem_rstr_orients_out      = elem_rstr_orients_in;
632     elem_rstr_curl_orients_out = elem_rstr_curl_orients_in;
633   }
634   local_num_entries = elem_size_out * num_comp_out * elem_size_in * num_comp_in * num_elem_in;
635 
636   // Loop over elements and put in data structure
637   // We store B_mat_in, B_mat_out, BTD, elem_mat in row-major order
638   CeedTensorContract contract;
639   CeedSize           count = 0;
640   CeedScalar        *vals, *BTD_mat = NULL, *elem_mat = NULL, *elem_mat_b = NULL;
641 
642   CeedCall(CeedBasisGetTensorContract(basis_in, &contract));
643   CeedCall(CeedCalloc(elem_size_out * num_qpts_in * num_eval_modes_in[0], &BTD_mat));
644   CeedCall(CeedCalloc(elem_size_out * elem_size_in, &elem_mat));
645   if (elem_rstr_curl_orients_in || elem_rstr_curl_orients_out) CeedCall(CeedCalloc(elem_size_out * elem_size_in, &elem_mat_b));
646 
647   CeedCall(CeedVectorGetArray(values, CEED_MEM_HOST, &vals));
648   for (CeedSize e = 0; e < num_elem_in; e++) {
649     for (CeedInt comp_in = 0; comp_in < num_comp_in; comp_in++) {
650       for (CeedInt comp_out = 0; comp_out < num_comp_out; comp_out++) {
651         // Compute B^T*D
652         for (CeedSize n = 0; n < elem_size_out; n++) {
653           for (CeedSize q = 0; q < num_qpts_in; q++) {
654             for (CeedInt e_in = 0; e_in < num_eval_modes_in[0]; e_in++) {
655               const CeedSize btd_index = n * (num_qpts_in * num_eval_modes_in[0]) + q * num_eval_modes_in[0] + e_in;
656               CeedScalar     sum       = 0.0;
657 
658               for (CeedInt e_out = 0; e_out < num_eval_modes_out[0]; e_out++) {
659                 const CeedSize b_out_index     = (q * num_eval_modes_out[0] + e_out) * elem_size_out + n;
660                 const CeedSize eval_mode_index = ((e_in * num_comp_in + comp_in) * num_eval_modes_out[0] + e_out) * num_comp_out + comp_out;
661                 const CeedSize qf_index        = q * layout_qf[0] + eval_mode_index * layout_qf[1] + e * layout_qf[2];
662 
663                 sum += B_mat_out[b_out_index] * assembled_qf_array[qf_index];
664               }
665               BTD_mat[btd_index] = sum;
666             }
667           }
668         }
669 
670         // Form element matrix itself (for each block component)
671         if (contract) {
672           CeedCall(CeedTensorContractApply(contract, 1, num_qpts_in * num_eval_modes_in[0], elem_size_in, elem_size_out, BTD_mat, CEED_NOTRANSPOSE,
673                                            false, B_mat_in, elem_mat));
674         } else {
675           CeedCall(CeedMatrixMatrixMultiply(ceed, BTD_mat, B_mat_in, elem_mat, elem_size_out, elem_size_in, num_qpts_in * num_eval_modes_in[0]));
676         }
677 
678         // Transform the element matrix if required
679         if (elem_rstr_orients_out) {
680           const bool *elem_orients = &elem_rstr_orients_out[e * elem_size_out];
681 
682           for (CeedInt i = 0; i < elem_size_out; i++) {
683             const double orient = elem_orients[i] ? -1.0 : 1.0;
684 
685             for (CeedInt j = 0; j < elem_size_in; j++) {
686               elem_mat[i * elem_size_in + j] *= orient;
687             }
688           }
689         } else if (elem_rstr_curl_orients_out) {
690           const CeedInt8 *elem_curl_orients = &elem_rstr_curl_orients_out[e * 3 * elem_size_out];
691 
692           // T^T*(B^T*D*B)
693           memcpy(elem_mat_b, elem_mat, elem_size_out * elem_size_in * sizeof(CeedScalar));
694           for (CeedInt i = 0; i < elem_size_out; i++) {
695             for (CeedInt j = 0; j < elem_size_in; j++) {
696               elem_mat[i * elem_size_in + j] = elem_mat_b[i * elem_size_in + j] * elem_curl_orients[3 * i + 1] +
697                                                (i > 0 ? elem_mat_b[(i - 1) * elem_size_in + j] * elem_curl_orients[3 * i - 1] : 0.0) +
698                                                (i < elem_size_out - 1 ? elem_mat_b[(i + 1) * elem_size_in + j] * elem_curl_orients[3 * i + 3] : 0.0);
699             }
700           }
701         }
702         if (elem_rstr_orients_in) {
703           const bool *elem_orients = &elem_rstr_orients_in[e * elem_size_in];
704 
705           for (CeedInt i = 0; i < elem_size_out; i++) {
706             for (CeedInt j = 0; j < elem_size_in; j++) {
707               elem_mat[i * elem_size_in + j] *= elem_orients[j] ? -1.0 : 1.0;
708             }
709           }
710         } else if (elem_rstr_curl_orients_in) {
711           const CeedInt8 *elem_curl_orients = &elem_rstr_curl_orients_in[e * 3 * elem_size_in];
712 
713           // (B^T*D*B)*T
714           memcpy(elem_mat_b, elem_mat, elem_size_out * elem_size_in * sizeof(CeedScalar));
715           for (CeedInt i = 0; i < elem_size_out; i++) {
716             for (CeedInt j = 0; j < elem_size_in; j++) {
717               elem_mat[i * elem_size_in + j] = elem_mat_b[i * elem_size_in + j] * elem_curl_orients[3 * j + 1] +
718                                                (j > 0 ? elem_mat_b[i * elem_size_in + j - 1] * elem_curl_orients[3 * j - 1] : 0.0) +
719                                                (j < elem_size_in - 1 ? elem_mat_b[i * elem_size_in + j + 1] * elem_curl_orients[3 * j + 3] : 0.0);
720             }
721           }
722         }
723 
724         // Put element matrix in coordinate data structure
725         for (CeedInt i = 0; i < elem_size_out; i++) {
726           for (CeedInt j = 0; j < elem_size_in; j++) {
727             vals[offset + count] = elem_mat[i * elem_size_in + j];
728             count++;
729           }
730         }
731       }
732     }
733   }
734   CeedCheck(count == local_num_entries, ceed, CEED_ERROR_MAJOR, "Error computing entries");
735   CeedCall(CeedVectorRestoreArray(values, &vals));
736 
737   // Cleanup
738   CeedCall(CeedFree(&BTD_mat));
739   CeedCall(CeedFree(&elem_mat));
740   CeedCall(CeedFree(&elem_mat_b));
741   if (elem_rstr_type_in == CEED_RESTRICTION_ORIENTED) {
742     CeedCall(CeedElemRestrictionRestoreOrientations(elem_rstr_in, &elem_rstr_orients_in));
743   } else if (elem_rstr_type_in == CEED_RESTRICTION_CURL_ORIENTED) {
744     CeedCall(CeedElemRestrictionRestoreCurlOrientations(elem_rstr_in, &elem_rstr_curl_orients_in));
745   }
746   if (elem_rstr_in != elem_rstr_out) {
747     if (elem_rstr_type_out == CEED_RESTRICTION_ORIENTED) {
748       CeedCall(CeedElemRestrictionRestoreOrientations(elem_rstr_out, &elem_rstr_orients_out));
749     } else if (elem_rstr_type_out == CEED_RESTRICTION_CURL_ORIENTED) {
750       CeedCall(CeedElemRestrictionRestoreCurlOrientations(elem_rstr_out, &elem_rstr_curl_orients_out));
751     }
752   }
753   CeedCall(CeedVectorRestoreArrayRead(assembled_qf, &assembled_qf_array));
754   CeedCall(CeedVectorDestroy(&assembled_qf));
755   return CEED_ERROR_SUCCESS;
756 }
757 
758 /**
759   @brief Count number of entries for assembled `CeedOperator`
760 
761   @param[in]  op          `CeedOperator` to assemble
762   @param[out] num_entries Number of entries in assembled representation
763 
764   @return An error code: 0 - success, otherwise - failure
765 
766   @ref Utility
767 **/
768 static int CeedSingleOperatorAssemblyCountEntries(CeedOperator op, CeedSize *num_entries) {
769   bool                is_composite;
770   CeedInt             num_elem_in, elem_size_in, num_comp_in, num_elem_out, elem_size_out, num_comp_out;
771   Ceed                ceed;
772   CeedElemRestriction rstr_in, rstr_out;
773 
774   CeedCall(CeedOperatorGetCeed(op, &ceed));
775   CeedCall(CeedOperatorIsComposite(op, &is_composite));
776   CeedCheck(!is_composite, ceed, CEED_ERROR_UNSUPPORTED, "Composite operator not supported");
777 
778   CeedCall(CeedOperatorGetActiveElemRestrictions(op, &rstr_in, &rstr_out));
779   CeedCall(CeedElemRestrictionGetNumElements(rstr_in, &num_elem_in));
780   CeedCall(CeedElemRestrictionGetElementSize(rstr_in, &elem_size_in));
781   CeedCall(CeedElemRestrictionGetNumComponents(rstr_in, &num_comp_in));
782   if (rstr_in != rstr_out) {
783     CeedCall(CeedElemRestrictionGetNumElements(rstr_out, &num_elem_out));
784     CeedCheck(num_elem_in == num_elem_out, ceed, CEED_ERROR_UNSUPPORTED,
785               "Active input and output operator restrictions must have the same number of elements");
786     CeedCall(CeedElemRestrictionGetElementSize(rstr_out, &elem_size_out));
787     CeedCall(CeedElemRestrictionGetNumComponents(rstr_out, &num_comp_out));
788   } else {
789     num_elem_out  = num_elem_in;
790     elem_size_out = elem_size_in;
791     num_comp_out  = num_comp_in;
792   }
793   *num_entries = (CeedSize)elem_size_in * num_comp_in * elem_size_out * num_comp_out * num_elem_in;
794   return CEED_ERROR_SUCCESS;
795 }
796 
797 /**
798   @brief Common code for creating a multigrid coarse `CeedOperator` and level transfer `CeedOperator` for a `CeedOperator`
799 
800   @param[in]  op_fine      Fine grid `CeedOperator`
801   @param[in]  p_mult_fine  L-vector multiplicity in parallel gather/scatter, or `NULL` if not creating prolongation/restriction `CeedOperator`
802   @param[in]  rstr_coarse  Coarse grid `CeedElemRestriction`
803   @param[in]  basis_coarse Coarse grid active vector `CeedBasis`
804   @param[in]  basis_c_to_f `CeedBasis` for coarse to fine interpolation, or `NULL` if not creating prolongation/restriction operators
805   @param[out] op_coarse    Coarse grid `CeedOperator`
806   @param[out] op_prolong   Coarse to fine `CeedOperator`, or `NULL`
807   @param[out] op_restrict  Fine to coarse `CeedOperator`, or `NULL`
808 
809   @return An error code: 0 - success, otherwise - failure
810 
811   @ref Developer
812 **/
813 static int CeedSingleOperatorMultigridLevel(CeedOperator op_fine, CeedVector p_mult_fine, CeedElemRestriction rstr_coarse, CeedBasis basis_coarse,
814                                             CeedBasis basis_c_to_f, CeedOperator *op_coarse, CeedOperator *op_prolong, CeedOperator *op_restrict) {
815   bool                is_composite;
816   Ceed                ceed;
817   CeedInt             num_comp, num_input_fields, num_output_fields;
818   CeedVector          mult_vec         = NULL;
819   CeedElemRestriction rstr_p_mult_fine = NULL, rstr_fine = NULL;
820   CeedOperatorField  *input_fields, *output_fields;
821 
822   CeedCall(CeedOperatorGetCeed(op_fine, &ceed));
823 
824   // Check for composite operator
825   CeedCall(CeedOperatorIsComposite(op_fine, &is_composite));
826   CeedCheck(!is_composite, ceed, CEED_ERROR_UNSUPPORTED, "Automatic multigrid setup for composite operators not supported");
827 
828   // Coarse Grid
829   CeedCall(CeedOperatorCreate(ceed, op_fine->qf, op_fine->dqf, op_fine->dqfT, op_coarse));
830   CeedCall(CeedOperatorGetFields(op_fine, &num_input_fields, &input_fields, &num_output_fields, &output_fields));
831   // -- Clone input fields
832   for (CeedInt i = 0; i < num_input_fields; i++) {
833     char               *field_name;
834     CeedVector          vec;
835     CeedElemRestriction rstr;
836     CeedBasis           basis;
837 
838     CeedCall(CeedOperatorFieldGetName(input_fields[i], &field_name));
839     CeedCall(CeedOperatorFieldGetVector(input_fields[i], &vec));
840     if (vec == CEED_VECTOR_ACTIVE) {
841       rstr  = rstr_coarse;
842       basis = basis_coarse;
843       CeedCall(CeedOperatorFieldGetElemRestriction(input_fields[i], &rstr_fine));
844     } else {
845       CeedCall(CeedOperatorFieldGetElemRestriction(input_fields[i], &rstr));
846       CeedCall(CeedOperatorFieldGetBasis(input_fields[i], &basis));
847     }
848     CeedCall(CeedOperatorSetField(*op_coarse, field_name, rstr, basis, vec));
849   }
850   // -- Clone output fields
851   for (CeedInt i = 0; i < num_output_fields; i++) {
852     char               *field_name;
853     CeedVector          vec;
854     CeedElemRestriction rstr;
855     CeedBasis           basis;
856 
857     CeedCall(CeedOperatorFieldGetName(output_fields[i], &field_name));
858     CeedCall(CeedOperatorFieldGetVector(output_fields[i], &vec));
859     if (vec == CEED_VECTOR_ACTIVE) {
860       rstr  = rstr_coarse;
861       basis = basis_coarse;
862       CeedCall(CeedOperatorFieldGetElemRestriction(output_fields[i], &rstr_fine));
863     } else {
864       CeedCall(CeedOperatorFieldGetElemRestriction(output_fields[i], &rstr));
865       CeedCall(CeedOperatorFieldGetBasis(output_fields[i], &basis));
866     }
867     CeedCall(CeedOperatorSetField(*op_coarse, field_name, rstr, basis, vec));
868   }
869   // -- Clone QFunctionAssemblyData
870   CeedCall(CeedQFunctionAssemblyDataReferenceCopy(op_fine->qf_assembled, &(*op_coarse)->qf_assembled));
871 
872   // Multiplicity vector
873   if (op_restrict || op_prolong) {
874     CeedVector          mult_e_vec;
875     CeedRestrictionType rstr_type;
876 
877     CeedCall(CeedElemRestrictionGetType(rstr_fine, &rstr_type));
878     CeedCheck(rstr_type != CEED_RESTRICTION_CURL_ORIENTED, ceed, CEED_ERROR_UNSUPPORTED,
879               "Element restrictions created with CeedElemRestrictionCreateCurlOriented are not supported");
880     CeedCheck(p_mult_fine, ceed, CEED_ERROR_INCOMPATIBLE, "Prolongation or restriction operator creation requires fine grid multiplicity vector");
881     CeedCall(CeedElemRestrictionCreateUnsignedCopy(rstr_fine, &rstr_p_mult_fine));
882     CeedCall(CeedElemRestrictionCreateVector(rstr_fine, &mult_vec, &mult_e_vec));
883     CeedCall(CeedVectorSetValue(mult_e_vec, 0.0));
884     CeedCall(CeedElemRestrictionApply(rstr_p_mult_fine, CEED_NOTRANSPOSE, p_mult_fine, mult_e_vec, CEED_REQUEST_IMMEDIATE));
885     CeedCall(CeedVectorSetValue(mult_vec, 0.0));
886     CeedCall(CeedElemRestrictionApply(rstr_p_mult_fine, CEED_TRANSPOSE, mult_e_vec, mult_vec, CEED_REQUEST_IMMEDIATE));
887     CeedCall(CeedVectorDestroy(&mult_e_vec));
888     CeedCall(CeedVectorReciprocal(mult_vec));
889   }
890 
891   // Clone name
892   bool   has_name = op_fine->name;
893   size_t name_len = op_fine->name ? strlen(op_fine->name) : 0;
894   CeedCall(CeedOperatorSetName(*op_coarse, op_fine->name));
895 
896   // Check that coarse to fine basis is provided if prolong/restrict operators are requested
897   CeedCheck(basis_c_to_f || (!op_restrict && !op_prolong), ceed, CEED_ERROR_INCOMPATIBLE,
898             "Prolongation or restriction operator creation requires coarse-to-fine basis");
899 
900   // Restriction/Prolongation Operators
901   CeedCall(CeedBasisGetNumComponents(basis_coarse, &num_comp));
902 
903   // Restriction
904   if (op_restrict) {
905     CeedInt             *num_comp_r_data;
906     CeedQFunctionContext ctx_r;
907     CeedQFunction        qf_restrict;
908 
909     CeedCall(CeedQFunctionCreateInteriorByName(ceed, "Scale", &qf_restrict));
910     CeedCall(CeedCalloc(1, &num_comp_r_data));
911     num_comp_r_data[0] = num_comp;
912     CeedCall(CeedQFunctionContextCreate(ceed, &ctx_r));
913     CeedCall(CeedQFunctionContextSetData(ctx_r, CEED_MEM_HOST, CEED_OWN_POINTER, sizeof(*num_comp_r_data), num_comp_r_data));
914     CeedCall(CeedQFunctionSetContext(qf_restrict, ctx_r));
915     CeedCall(CeedQFunctionContextDestroy(&ctx_r));
916     CeedCall(CeedQFunctionAddInput(qf_restrict, "input", num_comp, CEED_EVAL_NONE));
917     CeedCall(CeedQFunctionAddInput(qf_restrict, "scale", num_comp, CEED_EVAL_NONE));
918     CeedCall(CeedQFunctionAddOutput(qf_restrict, "output", num_comp, CEED_EVAL_INTERP));
919     CeedCall(CeedQFunctionSetUserFlopsEstimate(qf_restrict, num_comp));
920 
921     CeedCall(CeedOperatorCreate(ceed, qf_restrict, CEED_QFUNCTION_NONE, CEED_QFUNCTION_NONE, op_restrict));
922     CeedCall(CeedOperatorSetField(*op_restrict, "input", rstr_fine, CEED_BASIS_NONE, CEED_VECTOR_ACTIVE));
923     CeedCall(CeedOperatorSetField(*op_restrict, "scale", rstr_p_mult_fine, CEED_BASIS_NONE, mult_vec));
924     CeedCall(CeedOperatorSetField(*op_restrict, "output", rstr_coarse, basis_c_to_f, CEED_VECTOR_ACTIVE));
925 
926     // Set name
927     char *restriction_name;
928 
929     CeedCall(CeedCalloc(17 + name_len, &restriction_name));
930     sprintf(restriction_name, "restriction%s%s", has_name ? " for " : "", has_name ? op_fine->name : "");
931     CeedCall(CeedOperatorSetName(*op_restrict, restriction_name));
932     CeedCall(CeedFree(&restriction_name));
933 
934     // Check
935     CeedCall(CeedOperatorCheckReady(*op_restrict));
936 
937     // Cleanup
938     CeedCall(CeedQFunctionDestroy(&qf_restrict));
939   }
940 
941   // Prolongation
942   if (op_prolong) {
943     CeedInt             *num_comp_p_data;
944     CeedQFunctionContext ctx_p;
945     CeedQFunction        qf_prolong;
946 
947     CeedCall(CeedQFunctionCreateInteriorByName(ceed, "Scale", &qf_prolong));
948     CeedCall(CeedCalloc(1, &num_comp_p_data));
949     num_comp_p_data[0] = num_comp;
950     CeedCall(CeedQFunctionContextCreate(ceed, &ctx_p));
951     CeedCall(CeedQFunctionContextSetData(ctx_p, CEED_MEM_HOST, CEED_OWN_POINTER, sizeof(*num_comp_p_data), num_comp_p_data));
952     CeedCall(CeedQFunctionSetContext(qf_prolong, ctx_p));
953     CeedCall(CeedQFunctionContextDestroy(&ctx_p));
954     CeedCall(CeedQFunctionAddInput(qf_prolong, "input", num_comp, CEED_EVAL_INTERP));
955     CeedCall(CeedQFunctionAddInput(qf_prolong, "scale", num_comp, CEED_EVAL_NONE));
956     CeedCall(CeedQFunctionAddOutput(qf_prolong, "output", num_comp, CEED_EVAL_NONE));
957     CeedCall(CeedQFunctionSetUserFlopsEstimate(qf_prolong, num_comp));
958 
959     CeedCall(CeedOperatorCreate(ceed, qf_prolong, CEED_QFUNCTION_NONE, CEED_QFUNCTION_NONE, op_prolong));
960     CeedCall(CeedOperatorSetField(*op_prolong, "input", rstr_coarse, basis_c_to_f, CEED_VECTOR_ACTIVE));
961     CeedCall(CeedOperatorSetField(*op_prolong, "scale", rstr_p_mult_fine, CEED_BASIS_NONE, mult_vec));
962     CeedCall(CeedOperatorSetField(*op_prolong, "output", rstr_fine, CEED_BASIS_NONE, CEED_VECTOR_ACTIVE));
963 
964     // Set name
965     char *prolongation_name;
966 
967     CeedCall(CeedCalloc(18 + name_len, &prolongation_name));
968     sprintf(prolongation_name, "prolongation%s%s", has_name ? " for " : "", has_name ? op_fine->name : "");
969     CeedCall(CeedOperatorSetName(*op_prolong, prolongation_name));
970     CeedCall(CeedFree(&prolongation_name));
971 
972     // Check
973     CeedCall(CeedOperatorCheckReady(*op_prolong));
974 
975     // Cleanup
976     CeedCall(CeedQFunctionDestroy(&qf_prolong));
977   }
978 
979   // Check
980   CeedCall(CeedOperatorCheckReady(*op_coarse));
981 
982   // Cleanup
983   CeedCall(CeedVectorDestroy(&mult_vec));
984   CeedCall(CeedElemRestrictionDestroy(&rstr_p_mult_fine));
985   CeedCall(CeedBasisDestroy(&basis_c_to_f));
986   return CEED_ERROR_SUCCESS;
987 }
988 
989 /**
990   @brief Build 1D mass matrix and Laplacian with perturbation
991 
992   @param[in]  interp_1d   Interpolation matrix in one dimension
993   @param[in]  grad_1d     Gradient matrix in one dimension
994   @param[in]  q_weight_1d Quadrature weights in one dimension
995   @param[in]  P_1d        Number of basis nodes in one dimension
996   @param[in]  Q_1d        Number of quadrature points in one dimension
997   @param[in]  dim         Dimension of basis
998   @param[out] mass        Assembled mass matrix in one dimension
999   @param[out] laplace     Assembled perturbed Laplacian in one dimension
1000 
1001   @return An error code: 0 - success, otherwise - failure
1002 
1003   @ref Developer
1004 **/
1005 CeedPragmaOptimizeOff
1006 static int CeedBuildMassLaplace(const CeedScalar *interp_1d, const CeedScalar *grad_1d, const CeedScalar *q_weight_1d, CeedInt P_1d, CeedInt Q_1d,
1007                                 CeedInt dim, CeedScalar *mass, CeedScalar *laplace) {
1008   for (CeedInt i = 0; i < P_1d; i++) {
1009     for (CeedInt j = 0; j < P_1d; j++) {
1010       CeedScalar sum = 0.0;
1011       for (CeedInt k = 0; k < Q_1d; k++) sum += interp_1d[k * P_1d + i] * q_weight_1d[k] * interp_1d[k * P_1d + j];
1012       mass[i + j * P_1d] = sum;
1013     }
1014   }
1015   // -- Laplacian
1016   for (CeedInt i = 0; i < P_1d; i++) {
1017     for (CeedInt j = 0; j < P_1d; j++) {
1018       CeedScalar sum = 0.0;
1019 
1020       for (CeedInt k = 0; k < Q_1d; k++) sum += grad_1d[k * P_1d + i] * q_weight_1d[k] * grad_1d[k * P_1d + j];
1021       laplace[i + j * P_1d] = sum;
1022     }
1023   }
1024   CeedScalar perturbation = dim > 2 ? 1e-6 : 1e-4;
1025   for (CeedInt i = 0; i < P_1d; i++) laplace[i + P_1d * i] += perturbation;
1026   return CEED_ERROR_SUCCESS;
1027 }
1028 CeedPragmaOptimizeOn
1029 
1030 /// @}
1031 
1032 /// ----------------------------------------------------------------------------
1033 /// CeedOperator Backend API
1034 /// ----------------------------------------------------------------------------
1035 /// @addtogroup CeedOperatorBackend
1036 /// @{
1037 
1038 /**
1039   @brief Select correct basis matrix pointer based on @ref CeedEvalMode
1040 
1041   @param[in]  basis     `CeedBasis` from which to get the basis matrix
1042   @param[in]  eval_mode Current basis evaluation mode
1043   @param[in]  identity  Pointer to identity matrix
1044   @param[out] basis_ptr `CeedBasis` pointer to set
1045 
1046   @ref Backend
1047 **/
1048 int CeedOperatorGetBasisPointer(CeedBasis basis, CeedEvalMode eval_mode, const CeedScalar *identity, const CeedScalar **basis_ptr) {
1049   switch (eval_mode) {
1050     case CEED_EVAL_NONE:
1051       *basis_ptr = identity;
1052       break;
1053     case CEED_EVAL_INTERP:
1054       CeedCall(CeedBasisGetInterp(basis, basis_ptr));
1055       break;
1056     case CEED_EVAL_GRAD:
1057       CeedCall(CeedBasisGetGrad(basis, basis_ptr));
1058       break;
1059     case CEED_EVAL_DIV:
1060       CeedCall(CeedBasisGetDiv(basis, basis_ptr));
1061       break;
1062     case CEED_EVAL_CURL:
1063       CeedCall(CeedBasisGetCurl(basis, basis_ptr));
1064       break;
1065     case CEED_EVAL_WEIGHT:
1066       break;  // Caught by QF Assembly
1067   }
1068   assert(*basis_ptr != NULL);
1069   return CEED_ERROR_SUCCESS;
1070 }
1071 
1072 /**
1073   @brief Create point block restriction for active `CeedOperatorField`
1074 
1075   @param[in]  rstr             Original `CeedElemRestriction` for active field
1076   @param[out] point_block_rstr Address of the variable where the newly created `CeedElemRestriction` will be stored
1077 
1078   @return An error code: 0 - success, otherwise - failure
1079 
1080   @ref Backend
1081 **/
1082 int CeedOperatorCreateActivePointBlockRestriction(CeedElemRestriction rstr, CeedElemRestriction *point_block_rstr) {
1083   Ceed           ceed;
1084   CeedInt        num_elem, num_comp, shift, elem_size, comp_stride, *point_block_offsets;
1085   CeedSize       l_size;
1086   const CeedInt *offsets;
1087 
1088   CeedCall(CeedElemRestrictionGetCeed(rstr, &ceed));
1089   CeedCall(CeedElemRestrictionGetOffsets(rstr, CEED_MEM_HOST, &offsets));
1090 
1091   // Expand offsets
1092   CeedCall(CeedElemRestrictionGetNumElements(rstr, &num_elem));
1093   CeedCall(CeedElemRestrictionGetNumComponents(rstr, &num_comp));
1094   CeedCall(CeedElemRestrictionGetElementSize(rstr, &elem_size));
1095   CeedCall(CeedElemRestrictionGetCompStride(rstr, &comp_stride));
1096   CeedCall(CeedElemRestrictionGetLVectorSize(rstr, &l_size));
1097   shift = num_comp;
1098   if (comp_stride != 1) shift *= num_comp;
1099   CeedCall(CeedCalloc(num_elem * elem_size, &point_block_offsets));
1100   for (CeedInt i = 0; i < num_elem * elem_size; i++) {
1101     point_block_offsets[i] = offsets[i] * shift;
1102   }
1103 
1104   // Create new restriction
1105   CeedCall(CeedElemRestrictionCreate(ceed, num_elem, elem_size, num_comp * num_comp, 1, l_size * num_comp, CEED_MEM_HOST, CEED_OWN_POINTER,
1106                                      point_block_offsets, point_block_rstr));
1107 
1108   // Cleanup
1109   CeedCall(CeedElemRestrictionRestoreOffsets(rstr, &offsets));
1110   return CEED_ERROR_SUCCESS;
1111 }
1112 
1113 /**
1114   @brief Create object holding `CeedQFunction` assembly data for `CeedOperator`
1115 
1116   @param[in]  ceed `Ceed` object used to create the `CeedQFunctionAssemblyData`
1117   @param[out] data Address of the variable where the newly created `CeedQFunctionAssemblyData` will be stored
1118 
1119   @return An error code: 0 - success, otherwise - failure
1120 
1121   @ref Backend
1122 **/
1123 int CeedQFunctionAssemblyDataCreate(Ceed ceed, CeedQFunctionAssemblyData *data) {
1124   CeedCall(CeedCalloc(1, data));
1125   (*data)->ref_count = 1;
1126   (*data)->ceed      = ceed;
1127   CeedCall(CeedReference(ceed));
1128   return CEED_ERROR_SUCCESS;
1129 }
1130 
1131 /**
1132   @brief Increment the reference counter for a `CeedQFunctionAssemblyData`
1133 
1134   @param[in,out] data `CeedQFunctionAssemblyData` to increment the reference counter
1135 
1136   @return An error code: 0 - success, otherwise - failure
1137 
1138   @ref Backend
1139 **/
1140 int CeedQFunctionAssemblyDataReference(CeedQFunctionAssemblyData data) {
1141   data->ref_count++;
1142   return CEED_ERROR_SUCCESS;
1143 }
1144 
1145 /**
1146   @brief Set re-use of `CeedQFunctionAssemblyData`
1147 
1148   @param[in,out] data       `CeedQFunctionAssemblyData` to mark for reuse
1149   @param[in]     reuse_data Boolean flag indicating data re-use
1150 
1151   @return An error code: 0 - success, otherwise - failure
1152 
1153   @ref Backend
1154 **/
1155 int CeedQFunctionAssemblyDataSetReuse(CeedQFunctionAssemblyData data, bool reuse_data) {
1156   data->reuse_data        = reuse_data;
1157   data->needs_data_update = true;
1158   return CEED_ERROR_SUCCESS;
1159 }
1160 
1161 /**
1162   @brief Mark `CeedQFunctionAssemblyData` as stale
1163 
1164   @param[in,out] data              `CeedQFunctionAssemblyData` to mark as stale
1165   @param[in]     needs_data_update Boolean flag indicating if update is needed or completed
1166 
1167   @return An error code: 0 - success, otherwise - failure
1168 
1169   @ref Backend
1170 **/
1171 int CeedQFunctionAssemblyDataSetUpdateNeeded(CeedQFunctionAssemblyData data, bool needs_data_update) {
1172   data->needs_data_update = needs_data_update;
1173   return CEED_ERROR_SUCCESS;
1174 }
1175 
1176 /**
1177   @brief Determine if `CeedQFunctionAssemblyData` needs update
1178 
1179   @param[in]  data             `CeedQFunctionAssemblyData` to mark as stale
1180   @param[out] is_update_needed Boolean flag indicating if re-assembly is required
1181 
1182   @return An error code: 0 - success, otherwise - failure
1183 
1184   @ref Backend
1185 **/
1186 int CeedQFunctionAssemblyDataIsUpdateNeeded(CeedQFunctionAssemblyData data, bool *is_update_needed) {
1187   *is_update_needed = !data->reuse_data || data->needs_data_update;
1188   return CEED_ERROR_SUCCESS;
1189 }
1190 
1191 /**
1192   @brief Copy the pointer to a `CeedQFunctionAssemblyData`.
1193 
1194   Both pointers should be destroyed with @ref CeedQFunctionAssemblyDataDestroy().
1195 
1196   Note: If the value of ` *data_copy` passed to this function is non-`NULL` , then it is assumed that ` *data_copy` is a pointer to a `CeedQFunctionAssemblyData`.
1197         This `CeedQFunctionAssemblyData` will be destroyed if ` *data_copy` is the only reference to this `CeedQFunctionAssemblyData`.
1198 
1199   @param[in]     data      `CeedQFunctionAssemblyData` to copy reference to
1200   @param[in,out] data_copy Variable to store copied reference
1201 
1202   @return An error code: 0 - success, otherwise - failure
1203 
1204   @ref Backend
1205 **/
1206 int CeedQFunctionAssemblyDataReferenceCopy(CeedQFunctionAssemblyData data, CeedQFunctionAssemblyData *data_copy) {
1207   CeedCall(CeedQFunctionAssemblyDataReference(data));
1208   CeedCall(CeedQFunctionAssemblyDataDestroy(data_copy));
1209   *data_copy = data;
1210   return CEED_ERROR_SUCCESS;
1211 }
1212 
1213 /**
1214   @brief Get setup status for internal objects for `CeedQFunctionAssemblyData`
1215 
1216   @param[in]  data     `CeedQFunctionAssemblyData` to retrieve status
1217   @param[out] is_setup Boolean flag for setup status
1218 
1219   @return An error code: 0 - success, otherwise - failure
1220 
1221   @ref Backend
1222 **/
1223 int CeedQFunctionAssemblyDataIsSetup(CeedQFunctionAssemblyData data, bool *is_setup) {
1224   *is_setup = data->is_setup;
1225   return CEED_ERROR_SUCCESS;
1226 }
1227 
1228 /**
1229   @brief Set internal objects for `CeedQFunctionAssemblyData`
1230 
1231   @param[in,out] data `CeedQFunctionAssemblyData` to set objects
1232   @param[in]     vec  `CeedVector` to store assembled `CeedQFunction` at quadrature points
1233   @param[in]     rstr `CeedElemRestriction` for `CeedVector` containing assembled `CeedQFunction`
1234 
1235   @return An error code: 0 - success, otherwise - failure
1236 
1237   @ref Backend
1238 **/
1239 int CeedQFunctionAssemblyDataSetObjects(CeedQFunctionAssemblyData data, CeedVector vec, CeedElemRestriction rstr) {
1240   CeedCall(CeedVectorReferenceCopy(vec, &data->vec));
1241   CeedCall(CeedElemRestrictionReferenceCopy(rstr, &data->rstr));
1242 
1243   data->is_setup = true;
1244   return CEED_ERROR_SUCCESS;
1245 }
1246 
1247 /**
1248   @brief Get internal objects for `CeedQFunctionAssemblyData`
1249 
1250   @param[in,out] data `CeedQFunctionAssemblyData` to set objects
1251   @param[out]    vec  `CeedVector` to store assembled `CeedQFunction` at quadrature points
1252   @param[out]    rstr `CeedElemRestriction` for `CeedVector` containing assembled `CeedQFunction`
1253 
1254   @return An error code: 0 - success, otherwise - failure
1255 
1256   @ref Backend
1257 **/
1258 int CeedQFunctionAssemblyDataGetObjects(CeedQFunctionAssemblyData data, CeedVector *vec, CeedElemRestriction *rstr) {
1259   CeedCheck(data->is_setup, data->ceed, CEED_ERROR_INCOMPLETE, "Internal objects not set; must call CeedQFunctionAssemblyDataSetObjects first.");
1260 
1261   CeedCall(CeedVectorReferenceCopy(data->vec, vec));
1262   CeedCall(CeedElemRestrictionReferenceCopy(data->rstr, rstr));
1263   return CEED_ERROR_SUCCESS;
1264 }
1265 
1266 /**
1267   @brief Destroy `CeedQFunctionAssemblyData`
1268 
1269   @param[in,out] data  `CeedQFunctionAssemblyData` to destroy
1270 
1271   @return An error code: 0 - success, otherwise - failure
1272 
1273   @ref Backend
1274 **/
1275 int CeedQFunctionAssemblyDataDestroy(CeedQFunctionAssemblyData *data) {
1276   if (!*data || --(*data)->ref_count > 0) {
1277     *data = NULL;
1278     return CEED_ERROR_SUCCESS;
1279   }
1280   CeedCall(CeedDestroy(&(*data)->ceed));
1281   CeedCall(CeedVectorDestroy(&(*data)->vec));
1282   CeedCall(CeedElemRestrictionDestroy(&(*data)->rstr));
1283 
1284   CeedCall(CeedFree(data));
1285   return CEED_ERROR_SUCCESS;
1286 }
1287 
1288 /**
1289   @brief Get `CeedOperatorAssemblyData`
1290 
1291   @param[in]  op   `CeedOperator` to assemble
1292   @param[out] data `CeedQFunctionAssemblyData`
1293 
1294   @return An error code: 0 - success, otherwise - failure
1295 
1296   @ref Backend
1297 **/
1298 int CeedOperatorGetOperatorAssemblyData(CeedOperator op, CeedOperatorAssemblyData *data) {
1299   if (!op->op_assembled) {
1300     CeedOperatorAssemblyData data;
1301 
1302     CeedCall(CeedOperatorAssemblyDataCreate(op->ceed, op, &data));
1303     op->op_assembled = data;
1304   }
1305   *data = op->op_assembled;
1306   return CEED_ERROR_SUCCESS;
1307 }
1308 
1309 /**
1310   @brief Create object holding `CeedOperator` assembly data.
1311 
1312   The `CeedOperatorAssemblyData` holds an array with references to every active `CeedBasis` used in the `CeedOperator`.
1313   An array with references to the corresponding active `CeedElemRestriction` is also stored.
1314   For each active `CeedBasis, the `CeedOperatorAssemblyData` holds an array of all input and output @ref CeedEvalMode for this `CeedBasis`.
1315   The `CeedOperatorAssemblyData` holds an array of offsets for indexing into the assembled `CeedQFunction` arrays to the row representing each @ref CeedEvalMode.
1316   The number of input columns across all active bases for the assembled `CeedQFunction` is also stored.
1317   Lastly, the `CeedOperatorAssembly` data holds assembled matrices representing the full action of the `CeedBasis` for all @ref CeedEvalMode.
1318 
1319   @param[in]  ceed `Ceed` object used to create the `CeedOperatorAssemblyData`
1320   @param[in]  op   `CeedOperator` to be assembled
1321   @param[out] data Address of the variable where the newly created `CeedOperatorAssemblyData` will be stored
1322 
1323   @return An error code: 0 - success, otherwise - failure
1324 
1325   @ref Backend
1326 **/
1327 int CeedOperatorAssemblyDataCreate(Ceed ceed, CeedOperator op, CeedOperatorAssemblyData *data) {
1328   CeedInt             num_active_bases_in = 0, num_active_bases_out = 0, offset = 0;
1329   CeedInt             num_input_fields, *num_eval_modes_in = NULL, num_output_fields, *num_eval_modes_out = NULL;
1330   CeedSize          **eval_mode_offsets_in = NULL, **eval_mode_offsets_out = NULL;
1331   CeedEvalMode      **eval_modes_in = NULL, **eval_modes_out = NULL;
1332   CeedQFunctionField *qf_fields;
1333   CeedQFunction       qf;
1334   CeedOperatorField  *op_fields;
1335   bool                is_composite;
1336 
1337   CeedCall(CeedOperatorIsComposite(op, &is_composite));
1338   CeedCheck(!is_composite, ceed, CEED_ERROR_INCOMPATIBLE, "Can only create CeedOperator assembly data for non-composite operators.");
1339 
1340   // Allocate
1341   CeedCall(CeedCalloc(1, data));
1342   (*data)->ceed = ceed;
1343   CeedCall(CeedReference(ceed));
1344 
1345   // Build OperatorAssembly data
1346   CeedCall(CeedOperatorGetQFunction(op, &qf));
1347 
1348   // Determine active input basis
1349   CeedCall(CeedQFunctionGetFields(qf, &num_input_fields, &qf_fields, NULL, NULL));
1350   CeedCall(CeedOperatorGetFields(op, NULL, &op_fields, NULL, NULL));
1351   for (CeedInt i = 0; i < num_input_fields; i++) {
1352     CeedVector vec;
1353 
1354     CeedCall(CeedOperatorFieldGetVector(op_fields[i], &vec));
1355     if (vec == CEED_VECTOR_ACTIVE) {
1356       CeedInt      index = -1, num_comp, q_comp;
1357       CeedEvalMode eval_mode;
1358       CeedBasis    basis_in = NULL;
1359 
1360       CeedCall(CeedOperatorFieldGetBasis(op_fields[i], &basis_in));
1361       CeedCall(CeedQFunctionFieldGetEvalMode(qf_fields[i], &eval_mode));
1362       CeedCall(CeedBasisGetNumComponents(basis_in, &num_comp));
1363       CeedCall(CeedBasisGetNumQuadratureComponents(basis_in, eval_mode, &q_comp));
1364       for (CeedInt i = 0; i < num_active_bases_in; i++) {
1365         if ((*data)->active_bases_in[i] == basis_in) index = i;
1366       }
1367       if (index == -1) {
1368         CeedElemRestriction elem_rstr_in;
1369 
1370         index = num_active_bases_in;
1371         CeedCall(CeedRealloc(num_active_bases_in + 1, &(*data)->active_bases_in));
1372         (*data)->active_bases_in[num_active_bases_in] = NULL;
1373         CeedCall(CeedBasisReferenceCopy(basis_in, &(*data)->active_bases_in[num_active_bases_in]));
1374         CeedCall(CeedRealloc(num_active_bases_in + 1, &(*data)->active_elem_rstrs_in));
1375         (*data)->active_elem_rstrs_in[num_active_bases_in] = NULL;
1376         CeedCall(CeedOperatorFieldGetElemRestriction(op_fields[i], &elem_rstr_in));
1377         CeedCall(CeedElemRestrictionReferenceCopy(elem_rstr_in, &(*data)->active_elem_rstrs_in[num_active_bases_in]));
1378         CeedCall(CeedRealloc(num_active_bases_in + 1, &num_eval_modes_in));
1379         num_eval_modes_in[index] = 0;
1380         CeedCall(CeedRealloc(num_active_bases_in + 1, &eval_modes_in));
1381         eval_modes_in[index] = NULL;
1382         CeedCall(CeedRealloc(num_active_bases_in + 1, &eval_mode_offsets_in));
1383         eval_mode_offsets_in[index] = NULL;
1384         CeedCall(CeedRealloc(num_active_bases_in + 1, &(*data)->assembled_bases_in));
1385         (*data)->assembled_bases_in[index] = NULL;
1386         num_active_bases_in++;
1387       }
1388       if (eval_mode != CEED_EVAL_WEIGHT) {
1389         // q_comp = 1 if CEED_EVAL_NONE, CEED_EVAL_WEIGHT caught by QF Assembly
1390         CeedCall(CeedRealloc(num_eval_modes_in[index] + q_comp, &eval_modes_in[index]));
1391         CeedCall(CeedRealloc(num_eval_modes_in[index] + q_comp, &eval_mode_offsets_in[index]));
1392         for (CeedInt d = 0; d < q_comp; d++) {
1393           eval_modes_in[index][num_eval_modes_in[index] + d]        = eval_mode;
1394           eval_mode_offsets_in[index][num_eval_modes_in[index] + d] = offset;
1395           offset += num_comp;
1396         }
1397         num_eval_modes_in[index] += q_comp;
1398       }
1399     }
1400   }
1401 
1402   // Determine active output basis
1403   CeedCall(CeedQFunctionGetFields(qf, NULL, NULL, &num_output_fields, &qf_fields));
1404   CeedCall(CeedOperatorGetFields(op, NULL, NULL, NULL, &op_fields));
1405   offset = 0;
1406   for (CeedInt i = 0; i < num_output_fields; i++) {
1407     CeedVector vec;
1408 
1409     CeedCall(CeedOperatorFieldGetVector(op_fields[i], &vec));
1410     if (vec == CEED_VECTOR_ACTIVE) {
1411       CeedInt      index = -1, num_comp, q_comp;
1412       CeedEvalMode eval_mode;
1413       CeedBasis    basis_out = NULL;
1414 
1415       CeedCall(CeedOperatorFieldGetBasis(op_fields[i], &basis_out));
1416       CeedCall(CeedQFunctionFieldGetEvalMode(qf_fields[i], &eval_mode));
1417       CeedCall(CeedBasisGetNumComponents(basis_out, &num_comp));
1418       CeedCall(CeedBasisGetNumQuadratureComponents(basis_out, eval_mode, &q_comp));
1419       for (CeedInt i = 0; i < num_active_bases_out; i++) {
1420         if ((*data)->active_bases_out[i] == basis_out) index = i;
1421       }
1422       if (index == -1) {
1423         CeedElemRestriction elem_rstr_out;
1424 
1425         index = num_active_bases_out;
1426         CeedCall(CeedRealloc(num_active_bases_out + 1, &(*data)->active_bases_out));
1427         (*data)->active_bases_out[num_active_bases_out] = NULL;
1428         CeedCall(CeedBasisReferenceCopy(basis_out, &(*data)->active_bases_out[num_active_bases_out]));
1429         CeedCall(CeedRealloc(num_active_bases_out + 1, &(*data)->active_elem_rstrs_out));
1430         (*data)->active_elem_rstrs_out[num_active_bases_out] = NULL;
1431         CeedCall(CeedOperatorFieldGetElemRestriction(op_fields[i], &elem_rstr_out));
1432         CeedCall(CeedElemRestrictionReferenceCopy(elem_rstr_out, &(*data)->active_elem_rstrs_out[num_active_bases_out]));
1433         CeedCall(CeedRealloc(num_active_bases_out + 1, &num_eval_modes_out));
1434         num_eval_modes_out[index] = 0;
1435         CeedCall(CeedRealloc(num_active_bases_out + 1, &eval_modes_out));
1436         eval_modes_out[index] = NULL;
1437         CeedCall(CeedRealloc(num_active_bases_out + 1, &eval_mode_offsets_out));
1438         eval_mode_offsets_out[index] = NULL;
1439         CeedCall(CeedRealloc(num_active_bases_out + 1, &(*data)->assembled_bases_out));
1440         (*data)->assembled_bases_out[index] = NULL;
1441         num_active_bases_out++;
1442       }
1443       if (eval_mode != CEED_EVAL_WEIGHT) {
1444         // q_comp = 1 if CEED_EVAL_NONE, CEED_EVAL_WEIGHT caught by QF Assembly
1445         CeedCall(CeedRealloc(num_eval_modes_out[index] + q_comp, &eval_modes_out[index]));
1446         CeedCall(CeedRealloc(num_eval_modes_out[index] + q_comp, &eval_mode_offsets_out[index]));
1447         for (CeedInt d = 0; d < q_comp; d++) {
1448           eval_modes_out[index][num_eval_modes_out[index] + d]        = eval_mode;
1449           eval_mode_offsets_out[index][num_eval_modes_out[index] + d] = offset;
1450           offset += num_comp;
1451         }
1452         num_eval_modes_out[index] += q_comp;
1453       }
1454     }
1455   }
1456   (*data)->num_active_bases_in   = num_active_bases_in;
1457   (*data)->num_eval_modes_in     = num_eval_modes_in;
1458   (*data)->eval_modes_in         = eval_modes_in;
1459   (*data)->eval_mode_offsets_in  = eval_mode_offsets_in;
1460   (*data)->num_active_bases_out  = num_active_bases_out;
1461   (*data)->num_eval_modes_out    = num_eval_modes_out;
1462   (*data)->eval_modes_out        = eval_modes_out;
1463   (*data)->eval_mode_offsets_out = eval_mode_offsets_out;
1464   (*data)->num_output_components = offset;
1465   return CEED_ERROR_SUCCESS;
1466 }
1467 
1468 /**
1469   @brief Get `CeedOperator` @ref CeedEvalMode for assembly.
1470 
1471   Note: See @ref CeedOperatorAssemblyDataCreate() for a full description of the data stored in this object.
1472 
1473   @param[in]  data                  `CeedOperatorAssemblyData`
1474   @param[out] num_active_bases_in   Total number of active bases for input
1475   @param[out] num_eval_modes_in     Pointer to hold array of numbers of input @ref CeedEvalMode, or `NULL`.
1476                                       `eval_modes_in[0]` holds an array of eval modes for the first active `CeedBasis`.
1477   @param[out] eval_modes_in         Pointer to hold arrays of input @ref CeedEvalMode, or `NULL`
1478   @param[out] eval_mode_offsets_in  Pointer to hold arrays of input offsets at each quadrature point
1479   @param[out] num_active_bases_out  Total number of active bases for output
1480   @param[out] num_eval_modes_out    Pointer to hold array of numbers of output @ref CeedEvalMode, or `NULL`
1481   @param[out] eval_modes_out        Pointer to hold arrays of output @ref CeedEvalMode, or `NULL`
1482   @param[out] eval_mode_offsets_out Pointer to hold arrays of output offsets at each quadrature point
1483   @param[out] num_output_components The number of columns in the assembled `CeedQFunction` matrix for each quadrature point, including contributions of all active bases
1484 
1485   @return An error code: 0 - success, otherwise - failure
1486 
1487   @ref Backend
1488 **/
1489 int CeedOperatorAssemblyDataGetEvalModes(CeedOperatorAssemblyData data, CeedInt *num_active_bases_in, CeedInt **num_eval_modes_in,
1490                                          const CeedEvalMode ***eval_modes_in, CeedSize ***eval_mode_offsets_in, CeedInt *num_active_bases_out,
1491                                          CeedInt **num_eval_modes_out, const CeedEvalMode ***eval_modes_out, CeedSize ***eval_mode_offsets_out,
1492                                          CeedSize *num_output_components) {
1493   if (num_active_bases_in) *num_active_bases_in = data->num_active_bases_in;
1494   if (num_eval_modes_in) *num_eval_modes_in = data->num_eval_modes_in;
1495   if (eval_modes_in) *eval_modes_in = (const CeedEvalMode **)data->eval_modes_in;
1496   if (eval_mode_offsets_in) *eval_mode_offsets_in = data->eval_mode_offsets_in;
1497   if (num_active_bases_out) *num_active_bases_out = data->num_active_bases_out;
1498   if (num_eval_modes_out) *num_eval_modes_out = data->num_eval_modes_out;
1499   if (eval_modes_out) *eval_modes_out = (const CeedEvalMode **)data->eval_modes_out;
1500   if (eval_mode_offsets_out) *eval_mode_offsets_out = data->eval_mode_offsets_out;
1501   if (num_output_components) *num_output_components = data->num_output_components;
1502   return CEED_ERROR_SUCCESS;
1503 }
1504 
1505 /**
1506   @brief Get `CeedOperator` `CeedBasis` data for assembly.
1507 
1508   Note: See @ref CeedOperatorAssemblyDataCreate() for a full description of the data stored in this object.
1509 
1510   @param[in]  data                 `CeedOperatorAssemblyData`
1511   @param[out] num_active_bases_in  Number of active input bases, or `NULL`
1512   @param[out] active_bases_in      Pointer to hold active input `CeedBasis`, or `NULL`
1513   @param[out] assembled_bases_in   Pointer to hold assembled active input `B` , or `NULL`
1514   @param[out] num_active_bases_out Number of active output bases, or `NULL`
1515   @param[out] active_bases_out     Pointer to hold active output `CeedBasis`, or `NULL`
1516   @param[out] assembled_bases_out  Pointer to hold assembled active output `B` , or `NULL`
1517 
1518   @return An error code: 0 - success, otherwise - failure
1519 
1520   @ref Backend
1521 **/
1522 int CeedOperatorAssemblyDataGetBases(CeedOperatorAssemblyData data, CeedInt *num_active_bases_in, CeedBasis **active_bases_in,
1523                                      const CeedScalar ***assembled_bases_in, CeedInt *num_active_bases_out, CeedBasis **active_bases_out,
1524                                      const CeedScalar ***assembled_bases_out) {
1525   // Assemble B_in, B_out if needed
1526   if (assembled_bases_in && !data->assembled_bases_in[0]) {
1527     CeedInt num_qpts;
1528 
1529     if (data->active_bases_in[0] == CEED_BASIS_NONE) CeedCall(CeedElemRestrictionGetElementSize(data->active_elem_rstrs_in[0], &num_qpts));
1530     else CeedCall(CeedBasisGetNumQuadraturePoints(data->active_bases_in[0], &num_qpts));
1531     for (CeedInt b = 0; b < data->num_active_bases_in; b++) {
1532       bool        has_eval_none = false;
1533       CeedInt     num_nodes;
1534       CeedScalar *B_in = NULL, *identity = NULL;
1535 
1536       CeedCall(CeedElemRestrictionGetElementSize(data->active_elem_rstrs_in[b], &num_nodes));
1537       CeedCall(CeedCalloc(num_qpts * num_nodes * data->num_eval_modes_in[b], &B_in));
1538 
1539       for (CeedInt i = 0; i < data->num_eval_modes_in[b]; i++) {
1540         has_eval_none = has_eval_none || (data->eval_modes_in[b][i] == CEED_EVAL_NONE);
1541       }
1542       if (has_eval_none) {
1543         CeedCall(CeedCalloc(num_qpts * num_nodes, &identity));
1544         for (CeedInt i = 0; i < (num_nodes < num_qpts ? num_nodes : num_qpts); i++) {
1545           identity[i * num_nodes + i] = 1.0;
1546         }
1547       }
1548 
1549       for (CeedInt q = 0; q < num_qpts; q++) {
1550         for (CeedInt n = 0; n < num_nodes; n++) {
1551           CeedInt      d_in              = 0, q_comp_in;
1552           CeedEvalMode eval_mode_in_prev = CEED_EVAL_NONE;
1553 
1554           for (CeedInt e_in = 0; e_in < data->num_eval_modes_in[b]; e_in++) {
1555             const CeedInt     qq = data->num_eval_modes_in[b] * q;
1556             const CeedScalar *B  = NULL;
1557 
1558             CeedCall(CeedOperatorGetBasisPointer(data->active_bases_in[b], data->eval_modes_in[b][e_in], identity, &B));
1559             CeedCall(CeedBasisGetNumQuadratureComponents(data->active_bases_in[b], data->eval_modes_in[b][e_in], &q_comp_in));
1560             if (q_comp_in > 1) {
1561               if (e_in == 0 || data->eval_modes_in[b][e_in] != eval_mode_in_prev) d_in = 0;
1562               else B = &B[(++d_in) * num_qpts * num_nodes];
1563             }
1564             eval_mode_in_prev                 = data->eval_modes_in[b][e_in];
1565             B_in[(qq + e_in) * num_nodes + n] = B[q * num_nodes + n];
1566           }
1567         }
1568       }
1569       if (identity) CeedCall(CeedFree(&identity));
1570       data->assembled_bases_in[b] = B_in;
1571     }
1572   }
1573 
1574   if (assembled_bases_out && !data->assembled_bases_out[0]) {
1575     CeedInt num_qpts;
1576 
1577     if (data->active_bases_out[0] == CEED_BASIS_NONE) CeedCall(CeedElemRestrictionGetElementSize(data->active_elem_rstrs_out[0], &num_qpts));
1578     else CeedCall(CeedBasisGetNumQuadraturePoints(data->active_bases_out[0], &num_qpts));
1579     for (CeedInt b = 0; b < data->num_active_bases_out; b++) {
1580       bool        has_eval_none = false;
1581       CeedInt     num_nodes;
1582       CeedScalar *B_out = NULL, *identity = NULL;
1583 
1584       CeedCall(CeedElemRestrictionGetElementSize(data->active_elem_rstrs_out[b], &num_nodes));
1585       CeedCall(CeedCalloc(num_qpts * num_nodes * data->num_eval_modes_out[b], &B_out));
1586 
1587       for (CeedInt i = 0; i < data->num_eval_modes_out[b]; i++) {
1588         has_eval_none = has_eval_none || (data->eval_modes_out[b][i] == CEED_EVAL_NONE);
1589       }
1590       if (has_eval_none) {
1591         CeedCall(CeedCalloc(num_qpts * num_nodes, &identity));
1592         for (CeedInt i = 0; i < (num_nodes < num_qpts ? num_nodes : num_qpts); i++) {
1593           identity[i * num_nodes + i] = 1.0;
1594         }
1595       }
1596 
1597       for (CeedInt q = 0; q < num_qpts; q++) {
1598         for (CeedInt n = 0; n < num_nodes; n++) {
1599           CeedInt      d_out              = 0, q_comp_out;
1600           CeedEvalMode eval_mode_out_prev = CEED_EVAL_NONE;
1601 
1602           for (CeedInt e_out = 0; e_out < data->num_eval_modes_out[b]; e_out++) {
1603             const CeedInt     qq = data->num_eval_modes_out[b] * q;
1604             const CeedScalar *B  = NULL;
1605 
1606             CeedCall(CeedOperatorGetBasisPointer(data->active_bases_out[b], data->eval_modes_out[b][e_out], identity, &B));
1607             CeedCall(CeedBasisGetNumQuadratureComponents(data->active_bases_out[b], data->eval_modes_out[b][e_out], &q_comp_out));
1608             if (q_comp_out > 1) {
1609               if (e_out == 0 || data->eval_modes_out[b][e_out] != eval_mode_out_prev) d_out = 0;
1610               else B = &B[(++d_out) * num_qpts * num_nodes];
1611             }
1612             eval_mode_out_prev                  = data->eval_modes_out[b][e_out];
1613             B_out[(qq + e_out) * num_nodes + n] = B[q * num_nodes + n];
1614           }
1615         }
1616       }
1617       if (identity) CeedCall(CeedFree(&identity));
1618       data->assembled_bases_out[b] = B_out;
1619     }
1620   }
1621 
1622   // Pass out assembled data
1623   if (num_active_bases_in) *num_active_bases_in = data->num_active_bases_in;
1624   if (active_bases_in) *active_bases_in = data->active_bases_in;
1625   if (assembled_bases_in) *assembled_bases_in = (const CeedScalar **)data->assembled_bases_in;
1626   if (num_active_bases_out) *num_active_bases_out = data->num_active_bases_out;
1627   if (active_bases_out) *active_bases_out = data->active_bases_out;
1628   if (assembled_bases_out) *assembled_bases_out = (const CeedScalar **)data->assembled_bases_out;
1629   return CEED_ERROR_SUCCESS;
1630 }
1631 
1632 /**
1633   @brief Get `CeedOperator` `CeedBasis` data for assembly.
1634 
1635   Note: See @ref CeedOperatorAssemblyDataCreate() for a full description of the data stored in this object.
1636 
1637   @param[in]  data                      `CeedOperatorAssemblyData`
1638   @param[out] num_active_elem_rstrs_in  Number of active input element restrictions, or `NULL`
1639   @param[out] active_elem_rstrs_in      Pointer to hold active input `CeedElemRestriction`, or `NULL`
1640   @param[out] num_active_elem_rstrs_out Number of active output element restrictions, or `NULL`
1641   @param[out] active_elem_rstrs_out     Pointer to hold active output `CeedElemRestriction`, or `NULL`
1642 
1643   @return An error code: 0 - success, otherwise - failure
1644 
1645   @ref Backend
1646 **/
1647 int CeedOperatorAssemblyDataGetElemRestrictions(CeedOperatorAssemblyData data, CeedInt *num_active_elem_rstrs_in,
1648                                                 CeedElemRestriction **active_elem_rstrs_in, CeedInt *num_active_elem_rstrs_out,
1649                                                 CeedElemRestriction **active_elem_rstrs_out) {
1650   if (num_active_elem_rstrs_in) *num_active_elem_rstrs_in = data->num_active_bases_in;
1651   if (active_elem_rstrs_in) *active_elem_rstrs_in = data->active_elem_rstrs_in;
1652   if (num_active_elem_rstrs_out) *num_active_elem_rstrs_out = data->num_active_bases_out;
1653   if (active_elem_rstrs_out) *active_elem_rstrs_out = data->active_elem_rstrs_out;
1654   return CEED_ERROR_SUCCESS;
1655 }
1656 
1657 /**
1658   @brief Destroy `CeedOperatorAssemblyData`
1659 
1660   @param[in,out] data `CeedOperatorAssemblyData` to destroy
1661 
1662   @return An error code: 0 - success, otherwise - failure
1663 
1664   @ref Backend
1665 **/
1666 int CeedOperatorAssemblyDataDestroy(CeedOperatorAssemblyData *data) {
1667   if (!*data) {
1668     *data = NULL;
1669     return CEED_ERROR_SUCCESS;
1670   }
1671   CeedCall(CeedDestroy(&(*data)->ceed));
1672   for (CeedInt b = 0; b < (*data)->num_active_bases_in; b++) {
1673     CeedCall(CeedBasisDestroy(&(*data)->active_bases_in[b]));
1674     CeedCall(CeedElemRestrictionDestroy(&(*data)->active_elem_rstrs_in[b]));
1675     CeedCall(CeedFree(&(*data)->eval_modes_in[b]));
1676     CeedCall(CeedFree(&(*data)->eval_mode_offsets_in[b]));
1677     CeedCall(CeedFree(&(*data)->assembled_bases_in[b]));
1678   }
1679   for (CeedInt b = 0; b < (*data)->num_active_bases_out; b++) {
1680     CeedCall(CeedBasisDestroy(&(*data)->active_bases_out[b]));
1681     CeedCall(CeedElemRestrictionDestroy(&(*data)->active_elem_rstrs_out[b]));
1682     CeedCall(CeedFree(&(*data)->eval_modes_out[b]));
1683     CeedCall(CeedFree(&(*data)->eval_mode_offsets_out[b]));
1684     CeedCall(CeedFree(&(*data)->assembled_bases_out[b]));
1685   }
1686   CeedCall(CeedFree(&(*data)->active_bases_in));
1687   CeedCall(CeedFree(&(*data)->active_bases_out));
1688   CeedCall(CeedFree(&(*data)->active_elem_rstrs_in));
1689   CeedCall(CeedFree(&(*data)->active_elem_rstrs_out));
1690   CeedCall(CeedFree(&(*data)->num_eval_modes_in));
1691   CeedCall(CeedFree(&(*data)->num_eval_modes_out));
1692   CeedCall(CeedFree(&(*data)->eval_modes_in));
1693   CeedCall(CeedFree(&(*data)->eval_modes_out));
1694   CeedCall(CeedFree(&(*data)->eval_mode_offsets_in));
1695   CeedCall(CeedFree(&(*data)->eval_mode_offsets_out));
1696   CeedCall(CeedFree(&(*data)->assembled_bases_in));
1697   CeedCall(CeedFree(&(*data)->assembled_bases_out));
1698 
1699   CeedCall(CeedFree(data));
1700   return CEED_ERROR_SUCCESS;
1701 }
1702 
1703 /**
1704   @brief Retrieve fallback `CeedOperator` with a reference `Ceed` for advanced `CeedOperator` functionality
1705 
1706   @param[in]  op          `CeedOperator` to retrieve fallback for
1707   @param[out] op_fallback Fallback `CeedOperator`
1708 
1709   @return An error code: 0 - success, otherwise - failure
1710 
1711   @ref Backend
1712 **/
1713 int CeedOperatorGetFallback(CeedOperator op, CeedOperator *op_fallback) {
1714   // Create if needed
1715   if (!op->op_fallback) CeedCall(CeedOperatorCreateFallback(op));
1716   if (op->op_fallback) {
1717     bool is_debug;
1718     Ceed ceed;
1719 
1720     CeedCall(CeedOperatorGetCeed(op, &ceed));
1721     CeedCall(CeedIsDebug(ceed, &is_debug));
1722     if (is_debug) {
1723       Ceed        ceed_fallback;
1724       const char *resource, *resource_fallback;
1725 
1726       CeedCall(CeedGetOperatorFallbackCeed(ceed, &ceed_fallback));
1727       CeedCall(CeedGetResource(ceed, &resource));
1728       CeedCall(CeedGetResource(ceed_fallback, &resource_fallback));
1729 
1730       CeedDebug256(ceed, CEED_DEBUG_COLOR_SUCCESS, "---------- CeedOperator Fallback ----------\n");
1731       CeedDebug(ceed, "Falling back from %s operator at address %p to %s operator at address %p\n", resource, op, resource_fallback, op->op_fallback);
1732     }
1733   }
1734   *op_fallback = op->op_fallback;
1735   return CEED_ERROR_SUCCESS;
1736 }
1737 
1738 /**
1739   @brief Get the parent `CeedOperator` for a fallback `CeedOperator`
1740 
1741   @param[in]  op     `CeedOperator` context
1742   @param[out] parent Variable to store parent `CeedOperator` context
1743 
1744   @return An error code: 0 - success, otherwise - failure
1745 
1746   @ref Backend
1747 **/
1748 int CeedOperatorGetFallbackParent(CeedOperator op, CeedOperator *parent) {
1749   *parent = op->op_fallback_parent ? op->op_fallback_parent : NULL;
1750   return CEED_ERROR_SUCCESS;
1751 }
1752 
1753 /**
1754   @brief Get the `Ceed` context of the parent `CeedOperator` for a fallback `CeedOperator`
1755 
1756   @param[in]  op     `CeedOperator` context
1757   @param[out] parent Variable to store parent `Ceed` context
1758 
1759   @return An error code: 0 - success, otherwise - failure
1760 
1761   @ref Backend
1762 **/
1763 int CeedOperatorGetFallbackParentCeed(CeedOperator op, Ceed *parent) {
1764   *parent = op->op_fallback_parent ? op->op_fallback_parent->ceed : op->ceed;
1765   return CEED_ERROR_SUCCESS;
1766 }
1767 
1768 /// @}
1769 
1770 /// ----------------------------------------------------------------------------
1771 /// CeedOperator Public API
1772 /// ----------------------------------------------------------------------------
1773 /// @addtogroup CeedOperatorUser
1774 /// @{
1775 
1776 /**
1777   @brief Assemble a linear `CeedQFunction` associated with a `CeedOperator`.
1778 
1779   This returns a `CeedVector` containing a matrix at each quadrature point providing the action of the `CeedQFunction` associated with the `CeedOperator`.
1780   The vector `assembled` is of shape `[num_elements, num_input_fields, num_output_fields, num_quad_points]` and contains column-major matrices representing the action of the `CeedQFunction` for a corresponding quadrature point on an element.
1781 
1782   Inputs and outputs are in the order provided by the user when adding `CeedOperator` fields.
1783   For example, a `CeedQFunction` with inputs `u` and `gradu` and outputs `gradv` and `v` , provided in that order, would result in an assembled `CeedQFunction` that consists of `(1 + dim) x (dim + 1)` matrices at each quadrature point acting on the input ` [u, du_0, du_1]` and producing the output `[dv_0, dv_1, v]`.
1784 
1785   Note: Calling this function asserts that setup is complete and sets the `CeedOperator` as immutable.
1786 
1787   @param[in]  op        `CeedOperator` to assemble `CeedQFunction`
1788   @param[out] assembled `CeedVector` to store assembled `CeedQFunction` at quadrature points
1789   @param[out] rstr      `CeedElemRestriction` for `CeedVector` containing assembled `CeedQFunction`
1790   @param[in]  request   Address of @ref CeedRequest for non-blocking completion, else @ref CEED_REQUEST_IMMEDIATE
1791 
1792   @return An error code: 0 - success, otherwise - failure
1793 
1794   @ref User
1795 **/
1796 int CeedOperatorLinearAssembleQFunction(CeedOperator op, CeedVector *assembled, CeedElemRestriction *rstr, CeedRequest *request) {
1797   CeedCall(CeedOperatorCheckReady(op));
1798 
1799   if (op->LinearAssembleQFunction) {
1800     // Backend version
1801     CeedCall(op->LinearAssembleQFunction(op, assembled, rstr, request));
1802   } else {
1803     // Operator fallback
1804     Ceed         ceed;
1805     CeedOperator op_fallback;
1806 
1807     CeedCall(CeedOperatorGetCeed(op, &ceed));
1808     CeedCall(CeedOperatorGetFallback(op, &op_fallback));
1809     if (op_fallback) CeedCall(CeedOperatorLinearAssembleQFunction(op_fallback, assembled, rstr, request));
1810     else return CeedError(ceed, CEED_ERROR_UNSUPPORTED, "Backend does not support CeedOperatorLinearAssembleQFunction");
1811   }
1812   return CEED_ERROR_SUCCESS;
1813 }
1814 
1815 /**
1816   @brief Assemble `CeedQFunction` and store result internally.
1817 
1818   Return copied references of stored data to the caller.
1819   Caller is responsible for ownership and destruction of the copied references.
1820   See also @ref CeedOperatorLinearAssembleQFunction().
1821 
1822   Note: If the value of `assembled` or `rstr` passed to this function are non-`NULL` , then it is assumed that they hold valid pointers.
1823         These objects will be destroyed if `*assembled` or `*rstr` is the only reference to the object.
1824 
1825   @param[in]  op        `CeedOperator` to assemble `CeedQFunction`
1826   @param[out] assembled `CeedVector` to store assembled `CeedQFunction` at quadrature points
1827   @param[out] rstr      `CeedElemRestriction` for `CeedVector` containing assembled `CeedQFunction`
1828   @param[in]  request   Address of @ref CeedRequest for non-blocking completion, else @ref CEED_REQUEST_IMMEDIATE
1829 
1830   @return An error code: 0 - success, otherwise - failure
1831 
1832   @ref User
1833 **/
1834 int CeedOperatorLinearAssembleQFunctionBuildOrUpdate(CeedOperator op, CeedVector *assembled, CeedElemRestriction *rstr, CeedRequest *request) {
1835   int (*LinearAssembleQFunctionUpdate)(CeedOperator, CeedVector, CeedElemRestriction, CeedRequest *) = NULL;
1836   CeedOperator op_assemble                                                                           = NULL;
1837   CeedOperator op_fallback_parent                                                                    = NULL;
1838 
1839   CeedCall(CeedOperatorCheckReady(op));
1840 
1841   // Determine if fallback parent or operator has implementation
1842   CeedCall(CeedOperatorGetFallbackParent(op, &op_fallback_parent));
1843   if (op_fallback_parent && op_fallback_parent->LinearAssembleQFunctionUpdate) {
1844     // -- Backend version for op fallback parent is faster, if it exists
1845     LinearAssembleQFunctionUpdate = op_fallback_parent->LinearAssembleQFunctionUpdate;
1846     op_assemble                   = op_fallback_parent;
1847   } else if (op->LinearAssembleQFunctionUpdate) {
1848     // -- Backend version for op
1849     LinearAssembleQFunctionUpdate = op->LinearAssembleQFunctionUpdate;
1850     op_assemble                   = op;
1851   }
1852 
1853   // Assemble QFunction
1854   if (LinearAssembleQFunctionUpdate) {
1855     // Backend or fallback parent version
1856     bool                qf_assembled_is_setup;
1857     CeedVector          assembled_vec  = NULL;
1858     CeedElemRestriction assembled_rstr = NULL;
1859 
1860     CeedCall(CeedQFunctionAssemblyDataIsSetup(op->qf_assembled, &qf_assembled_is_setup));
1861     if (qf_assembled_is_setup) {
1862       bool update_needed;
1863 
1864       CeedCall(CeedQFunctionAssemblyDataGetObjects(op->qf_assembled, &assembled_vec, &assembled_rstr));
1865       CeedCall(CeedQFunctionAssemblyDataIsUpdateNeeded(op->qf_assembled, &update_needed));
1866       if (update_needed) CeedCall(LinearAssembleQFunctionUpdate(op_assemble, assembled_vec, assembled_rstr, request));
1867     } else {
1868       CeedCall(CeedOperatorLinearAssembleQFunction(op_assemble, &assembled_vec, &assembled_rstr, request));
1869       CeedCall(CeedQFunctionAssemblyDataSetObjects(op->qf_assembled, assembled_vec, assembled_rstr));
1870     }
1871     CeedCall(CeedQFunctionAssemblyDataSetUpdateNeeded(op->qf_assembled, false));
1872 
1873     // Copy reference from internally held copy
1874     CeedCall(CeedVectorReferenceCopy(assembled_vec, assembled));
1875     CeedCall(CeedElemRestrictionReferenceCopy(assembled_rstr, rstr));
1876     CeedCall(CeedVectorDestroy(&assembled_vec));
1877     CeedCall(CeedElemRestrictionDestroy(&assembled_rstr));
1878   } else {
1879     // Operator fallback
1880     Ceed         ceed;
1881     CeedOperator op_fallback;
1882 
1883     CeedCall(CeedOperatorGetCeed(op, &ceed));
1884     CeedCall(CeedOperatorGetFallback(op, &op_fallback));
1885     if (op_fallback) CeedCall(CeedOperatorLinearAssembleQFunctionBuildOrUpdate(op_fallback, assembled, rstr, request));
1886     else return CeedError(ceed, CEED_ERROR_UNSUPPORTED, "Backend does not support CeedOperatorLinearAssembleQFunctionUpdate");
1887   }
1888   return CEED_ERROR_SUCCESS;
1889 }
1890 
1891 /**
1892   @brief Assemble the diagonal of a square linear `CeedOperator`
1893 
1894   This overwrites a `CeedVector` with the diagonal of a linear `CeedOperator`.
1895 
1896   Note: Currently only non-composite `CeedOperator` with a single field and composite `CeedOperator` with single field sub-operators are supported.
1897 
1898   Note: Calling this function asserts that setup is complete and sets the `CeedOperator` as immutable.
1899 
1900   @param[in]  op        `CeedOperator` to assemble `CeedQFunction`
1901   @param[out] assembled `CeedVector` to store assembled `CeedOperator` diagonal
1902   @param[in]  request   Address of @ref CeedRequest for non-blocking completion, else @ref CEED_REQUEST_IMMEDIATE
1903 
1904   @return An error code: 0 - success, otherwise - failure
1905 
1906   @ref User
1907 **/
1908 int CeedOperatorLinearAssembleDiagonal(CeedOperator op, CeedVector assembled, CeedRequest *request) {
1909   bool     is_composite;
1910   CeedSize input_size = 0, output_size = 0;
1911   Ceed     ceed;
1912 
1913   CeedCall(CeedOperatorGetCeed(op, &ceed));
1914   CeedCall(CeedOperatorCheckReady(op));
1915   CeedCall(CeedOperatorIsComposite(op, &is_composite));
1916 
1917   CeedCall(CeedOperatorGetActiveVectorLengths(op, &input_size, &output_size));
1918   CeedCheck(input_size == output_size, ceed, CEED_ERROR_DIMENSION, "Operator must be square");
1919 
1920   // Early exit for empty operator
1921   if (!is_composite) {
1922     CeedInt num_elem = 0;
1923 
1924     CeedCall(CeedOperatorGetNumElements(op, &num_elem));
1925     if (num_elem == 0) return CEED_ERROR_SUCCESS;
1926   }
1927 
1928   if (op->LinearAssembleDiagonal) {
1929     // Backend version
1930     CeedCall(op->LinearAssembleDiagonal(op, assembled, request));
1931     return CEED_ERROR_SUCCESS;
1932   } else if (op->LinearAssembleAddDiagonal) {
1933     // Backend version with zeroing first
1934     CeedCall(CeedVectorSetValue(assembled, 0.0));
1935     CeedCall(op->LinearAssembleAddDiagonal(op, assembled, request));
1936     return CEED_ERROR_SUCCESS;
1937   } else {
1938     // Operator fallback
1939     CeedOperator op_fallback;
1940 
1941     CeedCall(CeedOperatorGetFallback(op, &op_fallback));
1942     if (op_fallback) {
1943       CeedCall(CeedOperatorLinearAssembleDiagonal(op_fallback, assembled, request));
1944       return CEED_ERROR_SUCCESS;
1945     }
1946   }
1947   // Default interface implementation
1948   CeedCall(CeedVectorSetValue(assembled, 0.0));
1949   CeedCall(CeedOperatorLinearAssembleAddDiagonal(op, assembled, request));
1950   return CEED_ERROR_SUCCESS;
1951 }
1952 
1953 /**
1954   @brief Assemble the diagonal of a square linear `CeedOperator`.
1955 
1956   This sums into a `CeedVector` the diagonal of a linear `CeedOperator`.
1957 
1958   Note: Currently only non-composite `CeedOperator` with a single field and composite `CeedOperator` with single field sub-operators are supported.
1959 
1960   Note: Calling this function asserts that setup is complete and sets the CeedOperator as immutable.
1961 
1962   @param[in]  op        `CeedOperator` to assemble `CeedQFunction`
1963   @param[out] assembled `CeedVector` to store assembled `CeedOperator` diagonal
1964   @param[in]  request   Address of @ref CeedRequest for non-blocking completion, else @ref CEED_REQUEST_IMMEDIATE
1965 
1966   @return An error code: 0 - success, otherwise - failure
1967 
1968   @ref User
1969 **/
1970 int CeedOperatorLinearAssembleAddDiagonal(CeedOperator op, CeedVector assembled, CeedRequest *request) {
1971   bool     is_composite;
1972   CeedSize input_size = 0, output_size = 0;
1973   Ceed     ceed;
1974 
1975   CeedCall(CeedOperatorGetCeed(op, &ceed));
1976   CeedCall(CeedOperatorCheckReady(op));
1977   CeedCall(CeedOperatorIsComposite(op, &is_composite));
1978 
1979   CeedCall(CeedOperatorGetActiveVectorLengths(op, &input_size, &output_size));
1980   CeedCheck(input_size == output_size, ceed, CEED_ERROR_DIMENSION, "Operator must be square");
1981 
1982   // Early exit for empty operator
1983   if (!is_composite) {
1984     CeedInt num_elem = 0;
1985 
1986     CeedCall(CeedOperatorGetNumElements(op, &num_elem));
1987     if (num_elem == 0) return CEED_ERROR_SUCCESS;
1988   }
1989 
1990   if (op->LinearAssembleAddDiagonal) {
1991     // Backend version
1992     CeedCall(op->LinearAssembleAddDiagonal(op, assembled, request));
1993     return CEED_ERROR_SUCCESS;
1994   } else {
1995     // Operator fallback
1996     CeedOperator op_fallback;
1997 
1998     CeedCall(CeedOperatorGetFallback(op, &op_fallback));
1999     if (op_fallback) {
2000       CeedCall(CeedOperatorLinearAssembleAddDiagonal(op_fallback, assembled, request));
2001       return CEED_ERROR_SUCCESS;
2002     }
2003   }
2004   // Default interface implementation
2005   if (is_composite) {
2006     CeedCall(CeedCompositeOperatorLinearAssembleAddDiagonal(op, request, false, assembled));
2007   } else {
2008     CeedCall(CeedSingleOperatorAssembleAddDiagonal_Core(op, request, false, assembled));
2009   }
2010   return CEED_ERROR_SUCCESS;
2011 }
2012 
2013 /**
2014    @brief Fully assemble the point-block diagonal pattern of a linear `CeedOperator`.
2015 
2016    Expected to be used in conjunction with @ref CeedOperatorLinearAssemblePointBlockDiagonal().
2017 
2018    The assembly routines use coordinate format, with `num_entries` tuples of the form `(i, j, value)` which indicate that value should be added to the matrix in entry `(i, j)`.
2019    Note that the `(i, j)` pairs are unique.
2020    This function returns the number of entries and their `(i, j)` locations, while @ref CeedOperatorLinearAssemblePointBlockDiagonal() provides the values in the same ordering.
2021 
2022    This will generally be slow unless your operator is low-order.
2023 
2024    Note: Calling this function asserts that setup is complete and sets the `CeedOperator` as immutable.
2025 
2026    @param[in]  op          `CeedOperator` to assemble
2027    @param[out] num_entries Number of entries in coordinate nonzero pattern
2028    @param[out] rows        Row number for each entry
2029    @param[out] cols        Column number for each entry
2030 
2031    @ref User
2032 **/
2033 int CeedOperatorLinearAssemblePointBlockDiagonalSymbolic(CeedOperator op, CeedSize *num_entries, CeedInt **rows, CeedInt **cols) {
2034   Ceed          ceed;
2035   bool          is_composite;
2036   CeedInt       num_active_components, num_sub_operators;
2037   CeedOperator *sub_operators;
2038 
2039   CeedCall(CeedOperatorGetCeed(op, &ceed));
2040   CeedCall(CeedOperatorIsComposite(op, &is_composite));
2041 
2042   CeedSize input_size = 0, output_size = 0;
2043   CeedCall(CeedOperatorGetActiveVectorLengths(op, &input_size, &output_size));
2044   CeedCheck(input_size == output_size, ceed, CEED_ERROR_DIMENSION, "Operator must be square");
2045 
2046   if (is_composite) {
2047     CeedCall(CeedCompositeOperatorGetNumSub(op, &num_sub_operators));
2048     CeedCall(CeedCompositeOperatorGetSubList(op, &sub_operators));
2049   } else {
2050     sub_operators     = &op;
2051     num_sub_operators = 1;
2052   }
2053 
2054   // Verify operator can be assembled correctly
2055   {
2056     CeedOperatorAssemblyData data;
2057     CeedInt                  num_active_elem_rstrs, comp_stride;
2058     CeedElemRestriction     *active_elem_rstrs;
2059 
2060     // Get initial values to check against
2061     CeedCall(CeedOperatorGetOperatorAssemblyData(sub_operators[0], &data));
2062     CeedCall(CeedOperatorAssemblyDataGetElemRestrictions(data, &num_active_elem_rstrs, &active_elem_rstrs, NULL, NULL));
2063     CeedCall(CeedElemRestrictionGetCompStride(active_elem_rstrs[0], &comp_stride));
2064     CeedCall(CeedElemRestrictionGetNumComponents(active_elem_rstrs[0], &num_active_components));
2065 
2066     // Verify that all active element restrictions have same component stride and number of components
2067     for (CeedInt k = 0; k < num_sub_operators; k++) {
2068       CeedCall(CeedOperatorGetOperatorAssemblyData(sub_operators[k], &data));
2069       CeedCall(CeedOperatorAssemblyDataGetElemRestrictions(data, &num_active_elem_rstrs, &active_elem_rstrs, NULL, NULL));
2070       for (CeedInt i = 0; i < num_active_elem_rstrs; i++) {
2071         CeedInt comp_stride_sub, num_active_components_sub;
2072 
2073         CeedCall(CeedElemRestrictionGetCompStride(active_elem_rstrs[i], &comp_stride_sub));
2074         CeedCheck(comp_stride == comp_stride_sub, ceed, CEED_ERROR_DIMENSION,
2075                   "Active element restrictions must have the same component stride: %d vs %d", comp_stride, comp_stride_sub);
2076         CeedCall(CeedElemRestrictionGetNumComponents(active_elem_rstrs[i], &num_active_components_sub));
2077         CeedCheck(num_active_components == num_active_components_sub, ceed, CEED_ERROR_INCOMPATIBLE,
2078                   "All suboperators must have the same number of output components");
2079       }
2080     }
2081   }
2082   *num_entries = input_size * num_active_components;
2083   CeedCall(CeedCalloc(*num_entries, rows));
2084   CeedCall(CeedCalloc(*num_entries, cols));
2085 
2086   for (CeedInt o = 0; o < num_sub_operators; o++) {
2087     CeedElemRestriction active_elem_rstr, point_block_active_elem_rstr;
2088     CeedInt             comp_stride, num_elem, elem_size;
2089     const CeedInt      *offsets, *point_block_offsets;
2090 
2091     CeedCall(CeedOperatorGetActiveElemRestriction(sub_operators[o], &active_elem_rstr));
2092     CeedCall(CeedElemRestrictionGetCompStride(active_elem_rstr, &comp_stride));
2093     CeedCall(CeedElemRestrictionGetNumElements(active_elem_rstr, &num_elem));
2094     CeedCall(CeedElemRestrictionGetElementSize(active_elem_rstr, &elem_size));
2095     CeedCall(CeedElemRestrictionGetOffsets(active_elem_rstr, CEED_MEM_HOST, &offsets));
2096 
2097     CeedCall(CeedOperatorCreateActivePointBlockRestriction(active_elem_rstr, &point_block_active_elem_rstr));
2098     CeedCall(CeedElemRestrictionGetOffsets(point_block_active_elem_rstr, CEED_MEM_HOST, &point_block_offsets));
2099 
2100     for (CeedSize i = 0; i < num_elem * elem_size; i++) {
2101       for (CeedInt c_out = 0; c_out < num_active_components; c_out++) {
2102         for (CeedInt c_in = 0; c_in < num_active_components; c_in++) {
2103           (*rows)[point_block_offsets[i] + c_out * num_active_components + c_in] = offsets[i] + c_out * comp_stride;
2104           (*cols)[point_block_offsets[i] + c_out * num_active_components + c_in] = offsets[i] + c_in * comp_stride;
2105         }
2106       }
2107     }
2108 
2109     CeedCall(CeedElemRestrictionRestoreOffsets(active_elem_rstr, &offsets));
2110     CeedCall(CeedElemRestrictionRestoreOffsets(point_block_active_elem_rstr, &point_block_offsets));
2111     CeedCall(CeedElemRestrictionDestroy(&point_block_active_elem_rstr));
2112   }
2113   return CEED_ERROR_SUCCESS;
2114 }
2115 
2116 /**
2117   @brief Assemble the point block diagonal of a square linear `CeedOperator`.
2118 
2119   This overwrites a `CeedVector` with the point block diagonal of a linear `CeedOperator`.
2120 
2121   Note: Currently only non-composite `CeedOperator` with a single field and composite `CeedOperator` with single field sub-operators are supported.
2122 
2123   Note: Calling this function asserts that setup is complete and sets the `CeedOperator` as immutable.
2124 
2125   @param[in]  op        `CeedOperator` to assemble `CeedQFunction`
2126   @param[out] assembled `CeedVector` to store assembled `CeedOperator` point block diagonal, provided in row-major form with an `num_comp * num_comp` block at each node.
2127                           The dimensions of this vector are derived from the active vector for the `CeedOperator`.
2128                           The array has shape `[nodes, component out, component in]`.
2129   @param[in]  request   Address of @ref CeedRequest for non-blocking completion, else @ref CEED_REQUEST_IMMEDIATE
2130 
2131   @return An error code: 0 - success, otherwise - failure
2132 
2133   @ref User
2134 **/
2135 int CeedOperatorLinearAssemblePointBlockDiagonal(CeedOperator op, CeedVector assembled, CeedRequest *request) {
2136   bool     is_composite;
2137   CeedSize input_size = 0, output_size = 0;
2138   Ceed     ceed;
2139 
2140   CeedCall(CeedOperatorGetCeed(op, &ceed));
2141   CeedCall(CeedOperatorCheckReady(op));
2142   CeedCall(CeedOperatorIsComposite(op, &is_composite));
2143 
2144   CeedCall(CeedOperatorGetActiveVectorLengths(op, &input_size, &output_size));
2145   CeedCheck(input_size == output_size, ceed, CEED_ERROR_DIMENSION, "Operator must be square");
2146 
2147   // Early exit for empty operator
2148   if (!is_composite) {
2149     CeedInt num_elem = 0;
2150 
2151     CeedCall(CeedOperatorGetNumElements(op, &num_elem));
2152     if (num_elem == 0) return CEED_ERROR_SUCCESS;
2153   }
2154 
2155   if (op->LinearAssemblePointBlockDiagonal) {
2156     // Backend version
2157     CeedCall(op->LinearAssemblePointBlockDiagonal(op, assembled, request));
2158     return CEED_ERROR_SUCCESS;
2159   } else if (op->LinearAssembleAddPointBlockDiagonal) {
2160     // Backend version with zeroing first
2161     CeedCall(CeedVectorSetValue(assembled, 0.0));
2162     CeedCall(CeedOperatorLinearAssembleAddPointBlockDiagonal(op, assembled, request));
2163     return CEED_ERROR_SUCCESS;
2164   } else {
2165     // Operator fallback
2166     CeedOperator op_fallback;
2167 
2168     CeedCall(CeedOperatorGetFallback(op, &op_fallback));
2169     if (op_fallback) {
2170       CeedCall(CeedOperatorLinearAssemblePointBlockDiagonal(op_fallback, assembled, request));
2171       return CEED_ERROR_SUCCESS;
2172     }
2173   }
2174   // Default interface implementation
2175   CeedCall(CeedVectorSetValue(assembled, 0.0));
2176   CeedCall(CeedOperatorLinearAssembleAddPointBlockDiagonal(op, assembled, request));
2177   return CEED_ERROR_SUCCESS;
2178 }
2179 
2180 /**
2181   @brief Assemble the point block diagonal of a square linear `CeedOperator`.
2182 
2183   This sums into a `CeedVector` with the point block diagonal of a linear `CeedOperator`.
2184 
2185   Note: Currently only non-composite `CeedOperator` with a single field and composite `CeedOperator` with single field sub-operators are supported.
2186 
2187   Note: Calling this function asserts that setup is complete and sets the `CeedOperator` as immutable.
2188 
2189   @param[in]  op        `CeedOperator` to assemble `CeedQFunction`
2190   @param[out] assembled `CeedVector` to store assembled CeedOperator point block diagonal, provided in row-major form with an `num_comp * num_comp` block at each node.
2191                           The dimensions of this vector are derived from the active vector for the `CeedOperator`.
2192                           The array has shape `[nodes, component out, component in]`.
2193   @param[in]  request   Address of @ref CeedRequest for non-blocking completion, else @ref CEED_REQUEST_IMMEDIATE
2194 
2195   @return An error code: 0 - success, otherwise - failure
2196 
2197   @ref User
2198 **/
2199 int CeedOperatorLinearAssembleAddPointBlockDiagonal(CeedOperator op, CeedVector assembled, CeedRequest *request) {
2200   bool     is_composite;
2201   CeedSize input_size = 0, output_size = 0;
2202   Ceed     ceed;
2203 
2204   CeedCall(CeedOperatorGetCeed(op, &ceed));
2205   CeedCall(CeedOperatorCheckReady(op));
2206   CeedCall(CeedOperatorIsComposite(op, &is_composite));
2207 
2208   CeedCall(CeedOperatorGetActiveVectorLengths(op, &input_size, &output_size));
2209   CeedCheck(input_size == output_size, ceed, CEED_ERROR_DIMENSION, "Operator must be square");
2210 
2211   // Early exit for empty operator
2212   if (!is_composite) {
2213     CeedInt num_elem = 0;
2214 
2215     CeedCall(CeedOperatorGetNumElements(op, &num_elem));
2216     if (num_elem == 0) return CEED_ERROR_SUCCESS;
2217   }
2218 
2219   if (op->LinearAssembleAddPointBlockDiagonal) {
2220     // Backend version
2221     CeedCall(op->LinearAssembleAddPointBlockDiagonal(op, assembled, request));
2222     return CEED_ERROR_SUCCESS;
2223   } else {
2224     // Operator fallback
2225     CeedOperator op_fallback;
2226 
2227     CeedCall(CeedOperatorGetFallback(op, &op_fallback));
2228     if (op_fallback) {
2229       CeedCall(CeedOperatorLinearAssembleAddPointBlockDiagonal(op_fallback, assembled, request));
2230       return CEED_ERROR_SUCCESS;
2231     }
2232   }
2233   // Default interface implementation
2234   if (is_composite) {
2235     CeedCall(CeedCompositeOperatorLinearAssembleAddDiagonal(op, request, true, assembled));
2236   } else {
2237     CeedCall(CeedSingleOperatorAssembleAddDiagonal_Core(op, request, true, assembled));
2238   }
2239   return CEED_ERROR_SUCCESS;
2240 }
2241 
2242 /**
2243    @brief Fully assemble the nonzero pattern of a linear `CeedOperator`.
2244 
2245    Expected to be used in conjunction with @ref CeedOperatorLinearAssemble().
2246 
2247    The assembly routines use coordinate format, with `num_entries` tuples of the form `(i, j, value)` which indicate that value should be added to the matrix in entry `(i, j)`.
2248    Note that the `(i, j)` pairs are not unique and may repeat.
2249    This function returns the number of entries and their `(i, j)` locations, while @ref CeedOperatorLinearAssemble() provides the values in the same ordering.
2250 
2251    This will generally be slow unless your operator is low-order.
2252 
2253    Note: Calling this function asserts that setup is complete and sets the `CeedOperator` as immutable.
2254 
2255    @param[in]  op          `CeedOperator` to assemble
2256    @param[out] num_entries Number of entries in coordinate nonzero pattern
2257    @param[out] rows        Row number for each entry
2258    @param[out] cols        Column number for each entry
2259 
2260    @ref User
2261 **/
2262 int CeedOperatorLinearAssembleSymbolic(CeedOperator op, CeedSize *num_entries, CeedInt **rows, CeedInt **cols) {
2263   bool          is_composite;
2264   CeedInt       num_suboperators, offset = 0;
2265   CeedSize      single_entries;
2266   CeedOperator *sub_operators;
2267 
2268   CeedCall(CeedOperatorCheckReady(op));
2269   CeedCall(CeedOperatorIsComposite(op, &is_composite));
2270 
2271   if (op->LinearAssembleSymbolic) {
2272     // Backend version
2273     CeedCall(op->LinearAssembleSymbolic(op, num_entries, rows, cols));
2274     return CEED_ERROR_SUCCESS;
2275   } else {
2276     // Operator fallback
2277     CeedOperator op_fallback;
2278 
2279     CeedCall(CeedOperatorGetFallback(op, &op_fallback));
2280     if (op_fallback) {
2281       CeedCall(CeedOperatorLinearAssembleSymbolic(op_fallback, num_entries, rows, cols));
2282       return CEED_ERROR_SUCCESS;
2283     }
2284   }
2285 
2286   // Default interface implementation
2287 
2288   // Count entries and allocate rows, cols arrays
2289   *num_entries = 0;
2290   if (is_composite) {
2291     CeedCall(CeedCompositeOperatorGetNumSub(op, &num_suboperators));
2292     CeedCall(CeedCompositeOperatorGetSubList(op, &sub_operators));
2293     for (CeedInt k = 0; k < num_suboperators; ++k) {
2294       CeedCall(CeedSingleOperatorAssemblyCountEntries(sub_operators[k], &single_entries));
2295       *num_entries += single_entries;
2296     }
2297   } else {
2298     CeedCall(CeedSingleOperatorAssemblyCountEntries(op, &single_entries));
2299     *num_entries += single_entries;
2300   }
2301   CeedCall(CeedCalloc(*num_entries, rows));
2302   CeedCall(CeedCalloc(*num_entries, cols));
2303 
2304   // Assemble nonzero locations
2305   if (is_composite) {
2306     CeedCall(CeedCompositeOperatorGetNumSub(op, &num_suboperators));
2307     CeedCall(CeedCompositeOperatorGetSubList(op, &sub_operators));
2308     for (CeedInt k = 0; k < num_suboperators; ++k) {
2309       CeedCall(CeedSingleOperatorAssembleSymbolic(sub_operators[k], offset, *rows, *cols));
2310       CeedCall(CeedSingleOperatorAssemblyCountEntries(sub_operators[k], &single_entries));
2311       offset += single_entries;
2312     }
2313   } else {
2314     CeedCall(CeedSingleOperatorAssembleSymbolic(op, offset, *rows, *cols));
2315   }
2316   return CEED_ERROR_SUCCESS;
2317 }
2318 
2319 /**
2320    @brief Fully assemble the nonzero entries of a linear operator.
2321 
2322    Expected to be used in conjunction with @ref CeedOperatorLinearAssembleSymbolic().
2323 
2324    The assembly routines use coordinate format, with `num_entries` tuples of the form `(i, j, value)` which indicate that value should be added to the matrix in entry `(i, j)`.
2325    Note that the `(i, j)` pairs are not unique and may repeat.
2326    This function returns the values of the nonzero entries to be added, their `(i, j)` locations are provided by @ref CeedOperatorLinearAssembleSymbolic().
2327 
2328    This will generally be slow unless your operator is low-order.
2329 
2330    Note: Calling this function asserts that setup is complete and sets the `CeedOperator` as immutable.
2331 
2332    @param[in]  op     `CeedOperator` to assemble
2333    @param[out] values Values to assemble into matrix
2334 
2335    @ref User
2336 **/
2337 int CeedOperatorLinearAssemble(CeedOperator op, CeedVector values) {
2338   bool          is_composite;
2339   CeedInt       num_suboperators, offset = 0;
2340   CeedSize      single_entries = 0;
2341   CeedOperator *sub_operators;
2342 
2343   CeedCall(CeedOperatorCheckReady(op));
2344   CeedCall(CeedOperatorIsComposite(op, &is_composite));
2345 
2346   // Early exit for empty operator
2347   if (!is_composite) {
2348     CeedInt num_elem = 0;
2349 
2350     CeedCall(CeedOperatorGetNumElements(op, &num_elem));
2351     if (num_elem == 0) return CEED_ERROR_SUCCESS;
2352   }
2353 
2354   if (op->LinearAssemble) {
2355     // Backend version
2356     CeedCall(op->LinearAssemble(op, values));
2357     return CEED_ERROR_SUCCESS;
2358   } else {
2359     // Operator fallback
2360     CeedOperator op_fallback;
2361 
2362     CeedCall(CeedOperatorGetFallback(op, &op_fallback));
2363     if (op_fallback) {
2364       CeedCall(CeedOperatorLinearAssemble(op_fallback, values));
2365       return CEED_ERROR_SUCCESS;
2366     }
2367   }
2368 
2369   // Default interface implementation
2370   CeedCall(CeedVectorSetValue(values, 0.0));
2371   if (is_composite) {
2372     CeedCall(CeedCompositeOperatorGetNumSub(op, &num_suboperators));
2373     CeedCall(CeedCompositeOperatorGetSubList(op, &sub_operators));
2374     for (CeedInt k = 0; k < num_suboperators; k++) {
2375       CeedCall(CeedSingleOperatorAssemble(sub_operators[k], offset, values));
2376       CeedCall(CeedSingleOperatorAssemblyCountEntries(sub_operators[k], &single_entries));
2377       offset += single_entries;
2378     }
2379   } else {
2380     CeedCall(CeedSingleOperatorAssemble(op, offset, values));
2381   }
2382   return CEED_ERROR_SUCCESS;
2383 }
2384 
2385 /**
2386   @brief Get the multiplicity of nodes across sub-operators in a composite `CeedOperator`.
2387 
2388   Note: Calling this function asserts that setup is complete and sets the `CeedOperator` as immutable.
2389 
2390   @param[in]  op               Composite `CeedOperator`
2391   @param[in]  num_skip_indices Number of sub-operators to skip
2392   @param[in]  skip_indices     Array of indices of sub-operators to skip
2393   @param[out] mult             Vector to store multiplicity (of size `l_size` )
2394 
2395   @return An error code: 0 - success, otherwise - failure
2396 
2397   @ref User
2398 **/
2399 int CeedCompositeOperatorGetMultiplicity(CeedOperator op, CeedInt num_skip_indices, CeedInt *skip_indices, CeedVector mult) {
2400   Ceed                ceed;
2401   CeedInt             num_suboperators;
2402   CeedSize            l_vec_len;
2403   CeedScalar         *mult_array;
2404   CeedVector          ones_l_vec;
2405   CeedElemRestriction elem_rstr, mult_elem_rstr;
2406   CeedOperator       *sub_operators;
2407 
2408   CeedCall(CeedOperatorCheckReady(op));
2409 
2410   CeedCall(CeedOperatorGetCeed(op, &ceed));
2411 
2412   // Zero mult vector
2413   CeedCall(CeedVectorSetValue(mult, 0.0));
2414 
2415   // Get suboperators
2416   CeedCall(CeedCompositeOperatorGetNumSub(op, &num_suboperators));
2417   CeedCall(CeedCompositeOperatorGetSubList(op, &sub_operators));
2418   if (num_suboperators == 0) return CEED_ERROR_SUCCESS;
2419 
2420   // Work vector
2421   CeedCall(CeedVectorGetLength(mult, &l_vec_len));
2422   CeedCall(CeedVectorCreate(ceed, l_vec_len, &ones_l_vec));
2423   CeedCall(CeedVectorSetValue(ones_l_vec, 1.0));
2424   CeedCall(CeedVectorGetArray(mult, CEED_MEM_HOST, &mult_array));
2425 
2426   // Compute multiplicity across suboperators
2427   for (CeedInt i = 0; i < num_suboperators; i++) {
2428     const CeedScalar *sub_mult_array;
2429     CeedVector        sub_mult_l_vec, ones_e_vec;
2430 
2431     // -- Check for suboperator to skip
2432     for (CeedInt j = 0; j < num_skip_indices; j++) {
2433       if (skip_indices[j] == i) continue;
2434     }
2435 
2436     // -- Sub operator multiplicity
2437     CeedCall(CeedOperatorGetActiveElemRestriction(sub_operators[i], &elem_rstr));
2438     CeedCall(CeedElemRestrictionCreateUnorientedCopy(elem_rstr, &mult_elem_rstr));
2439     CeedCall(CeedElemRestrictionCreateVector(mult_elem_rstr, &sub_mult_l_vec, &ones_e_vec));
2440     CeedCall(CeedVectorSetValue(sub_mult_l_vec, 0.0));
2441     CeedCall(CeedElemRestrictionApply(mult_elem_rstr, CEED_NOTRANSPOSE, ones_l_vec, ones_e_vec, CEED_REQUEST_IMMEDIATE));
2442     CeedCall(CeedElemRestrictionApply(mult_elem_rstr, CEED_TRANSPOSE, ones_e_vec, sub_mult_l_vec, CEED_REQUEST_IMMEDIATE));
2443     CeedCall(CeedVectorGetArrayRead(sub_mult_l_vec, CEED_MEM_HOST, &sub_mult_array));
2444     // ---- Flag every node present in the current suboperator
2445     for (CeedInt j = 0; j < l_vec_len; j++) {
2446       if (sub_mult_array[j] > 0.0) mult_array[j] += 1.0;
2447     }
2448     CeedCall(CeedVectorRestoreArrayRead(sub_mult_l_vec, &sub_mult_array));
2449     CeedCall(CeedVectorDestroy(&sub_mult_l_vec));
2450     CeedCall(CeedVectorDestroy(&ones_e_vec));
2451     CeedCall(CeedElemRestrictionDestroy(&mult_elem_rstr));
2452   }
2453   CeedCall(CeedVectorRestoreArray(mult, &mult_array));
2454   CeedCall(CeedVectorDestroy(&ones_l_vec));
2455   return CEED_ERROR_SUCCESS;
2456 }
2457 
2458 /**
2459   @brief Create a multigrid coarse `CeedOperator` and level transfer `CeedOperator` for a `CeedOperator`, creating the prolongation basis from the fine and coarse grid interpolation.
2460 
2461   Note: Calling this function asserts that setup is complete and sets all four `CeedOperator` as immutable.
2462 
2463   @param[in]  op_fine      Fine grid `CeedOperator`
2464   @param[in]  p_mult_fine  L-vector multiplicity in parallel gather/scatter, or `NULL` if not creating prolongation/restriction `CeedOperator`
2465   @param[in]  rstr_coarse  Coarse grid `CeedElemRestriction`
2466   @param[in]  basis_coarse Coarse grid active vector `CeedBasis`
2467   @param[out] op_coarse    Coarse grid `CeedOperator`
2468   @param[out] op_prolong   Coarse to fine `CeedOperator`, or `NULL`
2469   @param[out] op_restrict  Fine to coarse `CeedOperator`, or `NULL`
2470 
2471   @return An error code: 0 - success, otherwise - failure
2472 
2473   @ref User
2474 **/
2475 int CeedOperatorMultigridLevelCreate(CeedOperator op_fine, CeedVector p_mult_fine, CeedElemRestriction rstr_coarse, CeedBasis basis_coarse,
2476                                      CeedOperator *op_coarse, CeedOperator *op_prolong, CeedOperator *op_restrict) {
2477   CeedBasis basis_c_to_f = NULL;
2478 
2479   CeedCall(CeedOperatorCheckReady(op_fine));
2480 
2481   // Build prolongation matrix, if required
2482   if (op_prolong || op_restrict) {
2483     CeedBasis basis_fine;
2484 
2485     CeedCall(CeedOperatorGetActiveBasis(op_fine, &basis_fine));
2486     CeedCall(CeedBasisCreateProjection(basis_coarse, basis_fine, &basis_c_to_f));
2487   }
2488 
2489   // Core code
2490   CeedCall(CeedSingleOperatorMultigridLevel(op_fine, p_mult_fine, rstr_coarse, basis_coarse, basis_c_to_f, op_coarse, op_prolong, op_restrict));
2491   return CEED_ERROR_SUCCESS;
2492 }
2493 
2494 /**
2495   @brief Create a multigrid coarse `CeedOperator` and level transfer `CeedOperator` for a `CeedOperator` with a tensor basis for the active basis.
2496 
2497   Note: Calling this function asserts that setup is complete and sets all four `CeedOperator` as immutable.
2498 
2499   @param[in]  op_fine       Fine grid `CeedOperator`
2500   @param[in]  p_mult_fine   L-vector multiplicity in parallel gather/scatter, or `NULL` if not creating prolongation/restriction `CeedOperator`
2501   @param[in]  rstr_coarse   Coarse grid `CeedElemRestriction`
2502   @param[in]  basis_coarse  Coarse grid active vector `CeedBasis`
2503   @param[in]  interp_c_to_f Matrix for coarse to fine interpolation, or `NULL` if not creating prolongation/restriction `CeedOperator`
2504   @param[out] op_coarse     Coarse grid `CeedOperator`
2505   @param[out] op_prolong    Coarse to fine `CeedOperator`, or `NULL`
2506   @param[out] op_restrict   Fine to coarse `CeedOperator`, or `NULL`
2507 
2508   @return An error code: 0 - success, otherwise - failure
2509 
2510   @ref User
2511 **/
2512 int CeedOperatorMultigridLevelCreateTensorH1(CeedOperator op_fine, CeedVector p_mult_fine, CeedElemRestriction rstr_coarse, CeedBasis basis_coarse,
2513                                              const CeedScalar *interp_c_to_f, CeedOperator *op_coarse, CeedOperator *op_prolong,
2514                                              CeedOperator *op_restrict) {
2515   Ceed      ceed;
2516   CeedInt   Q_f, Q_c;
2517   CeedBasis basis_fine, basis_c_to_f = NULL;
2518 
2519   CeedCall(CeedOperatorCheckReady(op_fine));
2520   CeedCall(CeedOperatorGetCeed(op_fine, &ceed));
2521 
2522   // Check for compatible quadrature spaces
2523   CeedCall(CeedOperatorGetActiveBasis(op_fine, &basis_fine));
2524   CeedCall(CeedBasisGetNumQuadraturePoints(basis_fine, &Q_f));
2525   CeedCall(CeedBasisGetNumQuadraturePoints(basis_coarse, &Q_c));
2526   CeedCheck(Q_f == Q_c, ceed, CEED_ERROR_DIMENSION, "Bases must have compatible quadrature spaces");
2527 
2528   // Create coarse to fine basis, if required
2529   if (op_prolong || op_restrict) {
2530     CeedInt     dim, num_comp, num_nodes_c, P_1d_f, P_1d_c;
2531     CeedScalar *q_ref, *q_weight, *grad;
2532 
2533     // Check if interpolation matrix is provided
2534     CeedCheck(interp_c_to_f, ceed, CEED_ERROR_INCOMPATIBLE,
2535               "Prolongation or restriction operator creation requires coarse-to-fine interpolation matrix");
2536     CeedCall(CeedBasisGetDimension(basis_fine, &dim));
2537     CeedCall(CeedBasisGetNumComponents(basis_fine, &num_comp));
2538     CeedCall(CeedBasisGetNumNodes1D(basis_fine, &P_1d_f));
2539     CeedCall(CeedElemRestrictionGetElementSize(rstr_coarse, &num_nodes_c));
2540     P_1d_c = dim == 1 ? num_nodes_c : dim == 2 ? sqrt(num_nodes_c) : cbrt(num_nodes_c);
2541     CeedCall(CeedCalloc(P_1d_f, &q_ref));
2542     CeedCall(CeedCalloc(P_1d_f, &q_weight));
2543     CeedCall(CeedCalloc(P_1d_f * P_1d_c * dim, &grad));
2544     CeedCall(CeedBasisCreateTensorH1(ceed, dim, num_comp, P_1d_c, P_1d_f, interp_c_to_f, grad, q_ref, q_weight, &basis_c_to_f));
2545     CeedCall(CeedFree(&q_ref));
2546     CeedCall(CeedFree(&q_weight));
2547     CeedCall(CeedFree(&grad));
2548   }
2549 
2550   // Core code
2551   CeedCall(CeedSingleOperatorMultigridLevel(op_fine, p_mult_fine, rstr_coarse, basis_coarse, basis_c_to_f, op_coarse, op_prolong, op_restrict));
2552   return CEED_ERROR_SUCCESS;
2553 }
2554 
2555 /**
2556   @brief Create a multigrid coarse `CeedOperator` and level transfer `CeedOperator` for a `CeedOperator` with a non-tensor basis for the active vector
2557 
2558   Note: Calling this function asserts that setup is complete and sets all four `CeedOperator` as immutable.
2559 
2560   @param[in]  op_fine       Fine grid `CeedOperator`
2561   @param[in]  p_mult_fine   L-vector multiplicity in parallel gather/scatter, or `NULL` if not creating prolongation/restriction `CeedOperator`
2562   @param[in]  rstr_coarse   Coarse grid `CeedElemRestriction`
2563   @param[in]  basis_coarse  Coarse grid active vector `CeedBasis`
2564   @param[in]  interp_c_to_f Matrix for coarse to fine interpolation, or `NULL` if not creating prolongation/restriction `CeedOperator`
2565   @param[out] op_coarse     Coarse grid `CeedOperator`
2566   @param[out] op_prolong    Coarse to fine `CeedOperator`, or `NULL`
2567   @param[out] op_restrict   Fine to coarse `CeedOperator`, or `NULL`
2568 
2569   @return An error code: 0 - success, otherwise - failure
2570 
2571   @ref User
2572 **/
2573 int CeedOperatorMultigridLevelCreateH1(CeedOperator op_fine, CeedVector p_mult_fine, CeedElemRestriction rstr_coarse, CeedBasis basis_coarse,
2574                                        const CeedScalar *interp_c_to_f, CeedOperator *op_coarse, CeedOperator *op_prolong,
2575                                        CeedOperator *op_restrict) {
2576   Ceed      ceed;
2577   CeedInt   Q_f, Q_c;
2578   CeedBasis basis_fine, basis_c_to_f = NULL;
2579 
2580   CeedCall(CeedOperatorCheckReady(op_fine));
2581   CeedCall(CeedOperatorGetCeed(op_fine, &ceed));
2582 
2583   // Check for compatible quadrature spaces
2584   CeedCall(CeedOperatorGetActiveBasis(op_fine, &basis_fine));
2585   CeedCall(CeedBasisGetNumQuadraturePoints(basis_fine, &Q_f));
2586   CeedCall(CeedBasisGetNumQuadraturePoints(basis_coarse, &Q_c));
2587   CeedCheck(Q_f == Q_c, ceed, CEED_ERROR_DIMENSION, "Bases must have compatible quadrature spaces");
2588 
2589   // Coarse to fine basis
2590   if (op_prolong || op_restrict) {
2591     CeedInt          dim, num_comp, num_nodes_c, num_nodes_f;
2592     CeedScalar      *q_ref, *q_weight, *grad;
2593     CeedElemTopology topo;
2594 
2595     // Check if interpolation matrix is provided
2596     CeedCheck(interp_c_to_f, ceed, CEED_ERROR_INCOMPATIBLE,
2597               "Prolongation or restriction operator creation requires coarse-to-fine interpolation matrix");
2598     CeedCall(CeedBasisGetTopology(basis_fine, &topo));
2599     CeedCall(CeedBasisGetDimension(basis_fine, &dim));
2600     CeedCall(CeedBasisGetNumComponents(basis_fine, &num_comp));
2601     CeedCall(CeedBasisGetNumNodes(basis_fine, &num_nodes_f));
2602     CeedCall(CeedElemRestrictionGetElementSize(rstr_coarse, &num_nodes_c));
2603     CeedCall(CeedCalloc(num_nodes_f * dim, &q_ref));
2604     CeedCall(CeedCalloc(num_nodes_f, &q_weight));
2605     CeedCall(CeedCalloc(num_nodes_f * num_nodes_c * dim, &grad));
2606     CeedCall(CeedBasisCreateH1(ceed, topo, num_comp, num_nodes_c, num_nodes_f, interp_c_to_f, grad, q_ref, q_weight, &basis_c_to_f));
2607     CeedCall(CeedFree(&q_ref));
2608     CeedCall(CeedFree(&q_weight));
2609     CeedCall(CeedFree(&grad));
2610   }
2611 
2612   // Core code
2613   CeedCall(CeedSingleOperatorMultigridLevel(op_fine, p_mult_fine, rstr_coarse, basis_coarse, basis_c_to_f, op_coarse, op_prolong, op_restrict));
2614   return CEED_ERROR_SUCCESS;
2615 }
2616 
2617 /**
2618   @brief Build a FDM based approximate inverse for each element for a `CeedOperator`.
2619 
2620   This returns a `CeedOperator` and `CeedVector` to apply a Fast Diagonalization Method based approximate inverse.
2621   This function obtains the simultaneous diagonalization for the 1D mass and Laplacian operators, \f$M = V^T V, K = V^T S V\f$.
2622   The assembled `CeedQFunction` is used to modify the eigenvalues from simultaneous diagonalization and obtain an approximate inverse of the form \f$V^T \hat S V\f$.
2623   The `CeedOperator` must be linear and non-composite.
2624   The associated `CeedQFunction` must therefore also be linear.
2625 
2626   Note: Calling this function asserts that setup is complete and sets the `CeedOperator` as immutable.
2627 
2628   @param[in]  op      `CeedOperator` to create element inverses
2629   @param[out] fdm_inv `CeedOperator` to apply the action of a FDM based inverse for each element
2630   @param[in]  request Address of @ref CeedRequest for non-blocking completion, else @ref CEED_REQUEST_IMMEDIATE
2631 
2632   @return An error code: 0 - success, otherwise - failure
2633 
2634   @ref User
2635 **/
2636 int CeedOperatorCreateFDMElementInverse(CeedOperator op, CeedOperator *fdm_inv, CeedRequest *request) {
2637   Ceed                 ceed, ceed_parent;
2638   bool                 interp = false, grad = false, is_tensor_basis = true;
2639   CeedInt              num_input_fields, P_1d, Q_1d, num_nodes, num_qpts, dim, num_comp = 1, num_elem = 1;
2640   CeedSize             l_size = 1;
2641   CeedScalar          *mass, *laplace, *x, *fdm_interp, *lambda, *elem_avg;
2642   const CeedScalar    *interp_1d, *grad_1d, *q_weight_1d;
2643   CeedVector           q_data;
2644   CeedElemRestriction  rstr  = NULL, rstr_qd_i;
2645   CeedBasis            basis = NULL, fdm_basis;
2646   CeedQFunctionContext ctx_fdm;
2647   CeedQFunctionField  *qf_fields;
2648   CeedQFunction        qf, qf_fdm;
2649   CeedOperatorField   *op_fields;
2650 
2651   CeedCall(CeedOperatorCheckReady(op));
2652 
2653   if (op->CreateFDMElementInverse) {
2654     // Backend version
2655     CeedCall(op->CreateFDMElementInverse(op, fdm_inv, request));
2656     return CEED_ERROR_SUCCESS;
2657   } else {
2658     // Operator fallback
2659     CeedOperator op_fallback;
2660 
2661     CeedCall(CeedOperatorGetFallback(op, &op_fallback));
2662     if (op_fallback) {
2663       CeedCall(CeedOperatorCreateFDMElementInverse(op_fallback, fdm_inv, request));
2664       return CEED_ERROR_SUCCESS;
2665     }
2666   }
2667 
2668   // Default interface implementation
2669   CeedCall(CeedOperatorGetCeed(op, &ceed));
2670   CeedCall(CeedOperatorGetFallbackParentCeed(op, &ceed_parent));
2671   CeedCall(CeedOperatorGetQFunction(op, &qf));
2672 
2673   // Determine active input basis
2674   CeedCall(CeedOperatorGetFields(op, &num_input_fields, &op_fields, NULL, NULL));
2675   CeedCall(CeedQFunctionGetFields(qf, NULL, &qf_fields, NULL, NULL));
2676   for (CeedInt i = 0; i < num_input_fields; i++) {
2677     CeedVector vec;
2678 
2679     CeedCall(CeedOperatorFieldGetVector(op_fields[i], &vec));
2680     if (vec == CEED_VECTOR_ACTIVE) {
2681       CeedEvalMode eval_mode;
2682 
2683       CeedCall(CeedQFunctionFieldGetEvalMode(qf_fields[i], &eval_mode));
2684       interp = interp || eval_mode == CEED_EVAL_INTERP;
2685       grad   = grad || eval_mode == CEED_EVAL_GRAD;
2686       CeedCall(CeedOperatorFieldGetBasis(op_fields[i], &basis));
2687       CeedCall(CeedOperatorFieldGetElemRestriction(op_fields[i], &rstr));
2688     }
2689   }
2690   CeedCheck(basis, ceed, CEED_ERROR_BACKEND, "No active field set");
2691   CeedCall(CeedBasisGetNumNodes1D(basis, &P_1d));
2692   CeedCall(CeedBasisGetNumNodes(basis, &num_nodes));
2693   CeedCall(CeedBasisGetNumQuadraturePoints1D(basis, &Q_1d));
2694   CeedCall(CeedBasisGetNumQuadraturePoints(basis, &num_qpts));
2695   CeedCall(CeedBasisGetDimension(basis, &dim));
2696   CeedCall(CeedBasisGetNumComponents(basis, &num_comp));
2697   CeedCall(CeedElemRestrictionGetNumElements(rstr, &num_elem));
2698   CeedCall(CeedElemRestrictionGetLVectorSize(rstr, &l_size));
2699 
2700   // Build and diagonalize 1D Mass and Laplacian
2701   CeedCall(CeedBasisIsTensor(basis, &is_tensor_basis));
2702   CeedCheck(is_tensor_basis, ceed, CEED_ERROR_BACKEND, "FDMElementInverse only supported for tensor bases");
2703   CeedCall(CeedCalloc(P_1d * P_1d, &mass));
2704   CeedCall(CeedCalloc(P_1d * P_1d, &laplace));
2705   CeedCall(CeedCalloc(P_1d * P_1d, &x));
2706   CeedCall(CeedCalloc(P_1d * P_1d, &fdm_interp));
2707   CeedCall(CeedCalloc(P_1d, &lambda));
2708   // -- Build matrices
2709   CeedCall(CeedBasisGetInterp1D(basis, &interp_1d));
2710   CeedCall(CeedBasisGetGrad1D(basis, &grad_1d));
2711   CeedCall(CeedBasisGetQWeights(basis, &q_weight_1d));
2712   CeedCall(CeedBuildMassLaplace(interp_1d, grad_1d, q_weight_1d, P_1d, Q_1d, dim, mass, laplace));
2713 
2714   // -- Diagonalize
2715   CeedCall(CeedSimultaneousDiagonalization(ceed, laplace, mass, x, lambda, P_1d));
2716   CeedCall(CeedFree(&mass));
2717   CeedCall(CeedFree(&laplace));
2718   for (CeedInt i = 0; i < P_1d; i++) {
2719     for (CeedInt j = 0; j < P_1d; j++) fdm_interp[i + j * P_1d] = x[j + i * P_1d];
2720   }
2721   CeedCall(CeedFree(&x));
2722 
2723   {
2724     CeedInt             layout[3], num_modes = (interp ? 1 : 0) + (grad ? dim : 0);
2725     CeedScalar          max_norm = 0;
2726     const CeedScalar   *assembled_array, *q_weight_array;
2727     CeedVector          assembled = NULL, q_weight;
2728     CeedElemRestriction rstr_qf   = NULL;
2729 
2730     // Assemble QFunction
2731     CeedCall(CeedOperatorLinearAssembleQFunctionBuildOrUpdate(op, &assembled, &rstr_qf, request));
2732     CeedCall(CeedElemRestrictionGetELayout(rstr_qf, layout));
2733     CeedCall(CeedElemRestrictionDestroy(&rstr_qf));
2734     CeedCall(CeedVectorNorm(assembled, CEED_NORM_MAX, &max_norm));
2735 
2736     // Calculate element averages
2737     CeedCall(CeedVectorCreate(ceed_parent, num_qpts, &q_weight));
2738     CeedCall(CeedBasisApply(basis, 1, CEED_NOTRANSPOSE, CEED_EVAL_WEIGHT, CEED_VECTOR_NONE, q_weight));
2739     CeedCall(CeedVectorGetArrayRead(assembled, CEED_MEM_HOST, &assembled_array));
2740     CeedCall(CeedVectorGetArrayRead(q_weight, CEED_MEM_HOST, &q_weight_array));
2741     CeedCall(CeedCalloc(num_elem, &elem_avg));
2742     const CeedScalar qf_value_bound = max_norm * 100 * CEED_EPSILON;
2743 
2744     for (CeedInt e = 0; e < num_elem; e++) {
2745       CeedInt count = 0;
2746 
2747       for (CeedInt q = 0; q < num_qpts; q++) {
2748         for (CeedInt i = 0; i < num_comp * num_comp * num_modes * num_modes; i++) {
2749           if (fabs(assembled_array[q * layout[0] + i * layout[1] + e * layout[2]]) > qf_value_bound) {
2750             elem_avg[e] += assembled_array[q * layout[0] + i * layout[1] + e * layout[2]] / q_weight_array[q];
2751             count++;
2752           }
2753         }
2754       }
2755       if (count) {
2756         elem_avg[e] /= count;
2757       } else {
2758         elem_avg[e] = 1.0;
2759       }
2760     }
2761     CeedCall(CeedVectorRestoreArrayRead(assembled, &assembled_array));
2762     CeedCall(CeedVectorDestroy(&assembled));
2763     CeedCall(CeedVectorRestoreArrayRead(q_weight, &q_weight_array));
2764     CeedCall(CeedVectorDestroy(&q_weight));
2765   }
2766 
2767   // Build FDM diagonal
2768   {
2769     CeedScalar *q_data_array, *fdm_diagonal;
2770 
2771     CeedCall(CeedCalloc(num_comp * num_nodes, &fdm_diagonal));
2772     const CeedScalar fdm_diagonal_bound = num_nodes * CEED_EPSILON;
2773     for (CeedInt c = 0; c < num_comp; c++) {
2774       for (CeedInt n = 0; n < num_nodes; n++) {
2775         if (interp) fdm_diagonal[c * num_nodes + n] = 1.0;
2776         if (grad) {
2777           for (CeedInt d = 0; d < dim; d++) {
2778             CeedInt i = (n / CeedIntPow(P_1d, d)) % P_1d;
2779             fdm_diagonal[c * num_nodes + n] += lambda[i];
2780           }
2781         }
2782         if (fabs(fdm_diagonal[c * num_nodes + n]) < fdm_diagonal_bound) fdm_diagonal[c * num_nodes + n] = fdm_diagonal_bound;
2783       }
2784     }
2785     CeedCall(CeedVectorCreate(ceed_parent, num_elem * num_comp * num_nodes, &q_data));
2786     CeedCall(CeedVectorSetValue(q_data, 0.0));
2787     CeedCall(CeedVectorGetArrayWrite(q_data, CEED_MEM_HOST, &q_data_array));
2788     for (CeedInt e = 0; e < num_elem; e++) {
2789       for (CeedInt c = 0; c < num_comp; c++) {
2790         for (CeedInt n = 0; n < num_nodes; n++)
2791           q_data_array[(e * num_comp + c) * num_nodes + n] = 1. / (elem_avg[e] * fdm_diagonal[c * num_nodes + n]);
2792       }
2793     }
2794     CeedCall(CeedFree(&elem_avg));
2795     CeedCall(CeedFree(&fdm_diagonal));
2796     CeedCall(CeedVectorRestoreArray(q_data, &q_data_array));
2797   }
2798 
2799   // Setup FDM operator
2800   // -- Basis
2801   {
2802     CeedScalar *grad_dummy, *q_ref_dummy, *q_weight_dummy;
2803 
2804     CeedCall(CeedCalloc(P_1d * P_1d, &grad_dummy));
2805     CeedCall(CeedCalloc(P_1d, &q_ref_dummy));
2806     CeedCall(CeedCalloc(P_1d, &q_weight_dummy));
2807     CeedCall(CeedBasisCreateTensorH1(ceed_parent, dim, num_comp, P_1d, P_1d, fdm_interp, grad_dummy, q_ref_dummy, q_weight_dummy, &fdm_basis));
2808     CeedCall(CeedFree(&fdm_interp));
2809     CeedCall(CeedFree(&grad_dummy));
2810     CeedCall(CeedFree(&q_ref_dummy));
2811     CeedCall(CeedFree(&q_weight_dummy));
2812     CeedCall(CeedFree(&lambda));
2813   }
2814 
2815   // -- Restriction
2816   {
2817     CeedInt strides[3] = {1, num_nodes, num_nodes * num_comp};
2818     CeedCall(CeedElemRestrictionCreateStrided(ceed_parent, num_elem, num_nodes, num_comp, num_elem * num_comp * num_nodes, strides, &rstr_qd_i));
2819   }
2820 
2821   // -- QFunction
2822   CeedCall(CeedQFunctionCreateInteriorByName(ceed_parent, "Scale", &qf_fdm));
2823   CeedCall(CeedQFunctionAddInput(qf_fdm, "input", num_comp, CEED_EVAL_INTERP));
2824   CeedCall(CeedQFunctionAddInput(qf_fdm, "scale", num_comp, CEED_EVAL_NONE));
2825   CeedCall(CeedQFunctionAddOutput(qf_fdm, "output", num_comp, CEED_EVAL_INTERP));
2826   CeedCall(CeedQFunctionSetUserFlopsEstimate(qf_fdm, num_comp));
2827 
2828   // -- QFunction context
2829   {
2830     CeedInt *num_comp_data;
2831 
2832     CeedCall(CeedCalloc(1, &num_comp_data));
2833     num_comp_data[0] = num_comp;
2834     CeedCall(CeedQFunctionContextCreate(ceed, &ctx_fdm));
2835     CeedCall(CeedQFunctionContextSetData(ctx_fdm, CEED_MEM_HOST, CEED_OWN_POINTER, sizeof(*num_comp_data), num_comp_data));
2836   }
2837   CeedCall(CeedQFunctionSetContext(qf_fdm, ctx_fdm));
2838   CeedCall(CeedQFunctionContextDestroy(&ctx_fdm));
2839 
2840   // -- Operator
2841   CeedCall(CeedOperatorCreate(ceed_parent, qf_fdm, NULL, NULL, fdm_inv));
2842   CeedCall(CeedOperatorSetField(*fdm_inv, "input", rstr, fdm_basis, CEED_VECTOR_ACTIVE));
2843   CeedCall(CeedOperatorSetField(*fdm_inv, "scale", rstr_qd_i, CEED_BASIS_NONE, q_data));
2844   CeedCall(CeedOperatorSetField(*fdm_inv, "output", rstr, fdm_basis, CEED_VECTOR_ACTIVE));
2845 
2846   // Cleanup
2847   CeedCall(CeedVectorDestroy(&q_data));
2848   CeedCall(CeedBasisDestroy(&fdm_basis));
2849   CeedCall(CeedElemRestrictionDestroy(&rstr_qd_i));
2850   CeedCall(CeedQFunctionDestroy(&qf_fdm));
2851   return CEED_ERROR_SUCCESS;
2852 }
2853 
2854 /// @}
2855